मराठी

The value of sin50° – sin70° + sin10° is equal to ______.

Advertisements
Advertisements

प्रश्न

The value of sin50° – sin70° + sin10° is equal to ______.

पर्याय

  • 1

  • 0

  • `1/2`

  • 2

MCQ
रिकाम्या जागा भरा
Advertisements

उत्तर

The value of sin50° – sin70° + sin10° is equal to 0.

Explanation:

Given expression is sin50° – sin70° + sin10°

(sin50° – sin70°) + sin10° = `2cos  (50^circ + 70^circ)/2 . sin  (50^circ - 70^circ)/2 + sin 10^circ`

= 2cos60°.(–sin10°) + sin10°

= `-2 xx 1/2 sin10^circ +  sin10^circ`

= –sin10° + sin10°

= 0

shaalaa.com
Values of Trigonometric Functions at Multiples and Submultiples of an Angle
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 3: Trigonometric Functions - Exercise [पृष्ठ ५७]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 11
पाठ 3 Trigonometric Functions
Exercise | Q 49 | पृष्ठ ५७

संबंधित प्रश्‍न

Prove that: \[\sqrt{2 + \sqrt{2 + 2 \cos 4x}} = 2 \text{ cos } x\]

 

Prove that:  \[\frac{1 - \cos 2x + \sin 2x}{1 + \cos 2x + \sin 2x} = \tan x\]

 

Prove that: \[\cos^3 2x + 3 \cos 2x = 4\left( \cos^6 x - \sin^6 x \right)\]


Prove that: \[\cos^2 \left( \frac{\pi}{4} - x \right) - \sin^2 \left( \frac{\pi}{4} - x \right) = \sin 2x\]


Prove that:  \[\cos 4x = 1 - 8 \cos^2 x + 8 \cos^4 x\]

 


Show that: \[3 \left( \sin x - \cos x \right)^4 + 6 \left( \sin x + \cos \right)^2 + 4 \left( \sin^6 x + \cos^6 x \right) = 13\]


Prove that: \[\cos^6 A - \sin^6 A = \cos 2A\left( 1 - \frac{1}{4} \sin^2 2A \right)\]

 

Prove that:\[\tan\left( \frac{\pi}{4} + x \right) + \tan\left( \frac{\pi}{4} - x \right) = 2 \sec 2x\]

 

Prove that: \[\cos 4x - \cos 4\alpha = 8 \left( \cos x - \cos \alpha \right) \left( \cos x + \cos \alpha \right) \left( \cos x - \sin \alpha \right) \left( \cos x + \sin \alpha \right)\]


\[\tan 82\frac{1° }{2} = \left( \sqrt{3} + \sqrt{2} \right) \left( \sqrt{2} + 1 \right) = \sqrt{2} + \sqrt{3} + \sqrt{4} + \sqrt{6}\]

 


 If 0 ≤ x ≤ π and x lies in the IInd quadrant such that  \[\sin x = \frac{1}{4}\]. Find the values of \[\cos\frac{x}{2}, \sin\frac{x}{2} \text{ and }  \tan\frac{x}{2}\]

 

 


Prove that: \[\cos \frac{\pi}{65} \cos \frac{2\pi}{65} \cos\frac{4\pi}{65} \cos\frac{8\pi}{65} \cos\frac{16\pi}{65} \cos\frac{32\pi}{65} = \frac{1}{64}\]

 

If \[2 \tan\frac{\alpha}{2} = \tan\frac{\beta}{2}\] , prove that \[\cos \alpha = \frac{3 + 5 \cos \beta}{5 + 3 \cos \beta}\]

 

 


Prove that:  \[\sin 5x = 5 \sin x - 20 \sin^3 x + 16 \sin^5 x\]

 

Prove that: \[4 \left( \cos^3 10 °+ \sin^3 20° \right) = 3 \left( \cos 10°+ \sin 2° \right)\]

 

Prove that `tan x + tan (π/3 + x) - tan(π/3 - x) = 3tan 3x`


\[\cot x + \cot\left( \frac{\pi}{3} + x \right) + \cot\left( \frac{2\pi}{3} + x \right) = 3 \cot 3x\] 


\[\sin^3 x + \sin^3 \left( \frac{2\pi}{3} + x \right) + \sin^3 \left( \frac{4\pi}{3} + x \right) = - \frac{3}{4} \sin 3x\]

 


Prove that:  \[\sin^2 42° - \cos^2 78 = \frac{\sqrt{5} + 1}{8}\] 

 

Prove that: \[\cos\frac{\pi}{15}\cos\frac{2\pi}{15}\cos\frac{4\pi}{15}\cos\frac{7\pi}{15} = \frac{1}{16}\]

 

Prove that: \[\cos 6° \cos 42°   \cos 66°    \cos 78° = \frac{1}{16}\]

 

Prove that: \[\cos 36° \cos 42° \cos 60° \cos 78°  = \frac{1}{16}\]

 

Prove that: \[\sin\frac{\pi}{5}\sin\frac{2\pi}{5}\sin\frac{3\pi}{5}\sin\frac{4\pi}{5} = \frac{5}{16}\]

 

Prove that: \[\cos\frac{\pi}{15} \cos \frac{2\pi}{15} \cos \frac{3\pi}{15} \cos \frac{4\pi}{15} \cos \frac{5\pi}{15} \cos\frac{6\pi}{15} \cos \frac{7\pi}{15} = \frac{1}{128}\]

 

If \[\frac{\pi}{2} < x < \pi,\] the write the value of \[\sqrt{2 + \sqrt{2 + 2 \cos 2x}}\] in the simplest form.

 
 

If  \[\text{ sin } x + \text{ cos } x = a\], then find the value of

\[\sin^6 x + \cos^6 x\] .
 

 


If \[\cos x = \frac{1}{2} \left( a + \frac{1}{a} \right),\]  and \[\cos 3 x = \lambda \left( a^3 + \frac{1}{a^3} \right)\] then \[\lambda =\]

 

 


If  \[2 \tan \alpha = 3 \tan \beta, \text{ then }  \tan \left( \alpha - \beta \right) =\]

 


If \[\tan \alpha = \frac{1 - \cos \beta}{\sin \beta}\] , then

 

If \[A = 2 \sin^2 x - \cos 2x\] , then A lies in the interval


If \[\tan \left( \pi/4 + x \right) + \tan \left( \pi/4 - x \right) = \lambda \sec 2x, \text{ then } \]


If α and β are acute angles satisfying \[\cos 2 \alpha = \frac{3 \cos 2 \beta - 1}{3 - \cos 2 \beta}\] , then tan α =

 

If  \[\left( 2^n + 1 \right) x = \pi,\] then \[2^n \cos x \cos 2x \cos 2^2 x . . . \cos 2^{n - 1} x = 1\]

 


The value of \[\cos \left( 36°  - A \right) \cos \left( 36° + A \right) + \cos \left( 54°  - A \right) \cos \left( 54°  + A \right)\] is 

 

If A = cos2θ + sin4θ for all values of θ, then prove that `3/4` ≤ A ≤ 1.


If acos2θ + bsin2θ = c has α and β as its roots, then prove that tanα + tanβ = `(2b)/(a + c)`.

`["Hint: Use the identities" cos2theta = (1 - tan^2theta)/(1 + tan^2theta) "and" sin2theta =  (2tantheta)/(1 + tan^2theta)]`.


If tanθ = `1/2` and tanΦ = `1/3`, then the value of θ + Φ is ______.


The value of `(1 - tan^2 15^circ)/(1 + tan^2 15^circ)` is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×