हिंदी
तमिलनाडु बोर्ड ऑफ सेकेंडरी एज्युकेशनएचएससी विज्ञान कक्षा ११

Solve the following equations:cos 2θ = 5+14

Advertisements
Advertisements

प्रश्न

Solve the following equations:
cos 2θ = `(sqrt(5) + 1)/4`

योग
Advertisements

उत्तर

We know cos 36° = `(sqrt(5) + 1)/4`, 36° = `pi/5`

cos 2θ = cos 36° = `cos (pi/5)`

The general solution is

2θ = `2"n"pi +- pi/5`, n ∈ Z

 θ = `"n"pi +- pi/10`, n ∈ Z

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 3: Trigonometry - Exercise 3.8 [पृष्ठ १३३]

APPEARS IN

सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 11 TN Board
अध्याय 3 Trigonometry
Exercise 3.8 | Q 3. (x) | पृष्ठ १३३

संबंधित प्रश्न

Prove that

\[\frac{cosec(90^\circ + x) + \cot(450^\circ + x)}{cosec(90^\circ - x) + \tan(180^\circ - x)} + \frac{\tan(180^\circ + x) + \sec(180^\circ - x)}{\tan(360^\circ + x) - \sec( - x)} = 2\]

 


Prove that

\[\left\{ 1 + \cot x - \sec\left( \frac{\pi}{2} + x \right) \right\}\left\{ 1 + \cot x + \sec\left( \frac{\pi}{2} + x \right) \right\} = 2\cot x\]

 


Prove that:

\[\sin\frac{10\pi}{3}\cos\frac{13\pi}{6} + \cos\frac{8\pi}{3}\sin\frac{5\pi}{6} = - 1\]

If \[\frac{\pi}{2} < x < \frac{3\pi}{2},\text{ then }\sqrt{\frac{1 - \sin x}{1 + \sin x}}\] is equal to

 


If \[\frac{\pi}{2} < x < \pi, \text{ then }\sqrt{\frac{1 - \sin x}{1 + \sin x}} + \sqrt{\frac{1 + \sin x}{1 - \sin x}}\] is equal to


If x = r sin θ cos ϕ, y = r sin θ sin ϕ and r cos θ, then x2 + y2 + z2 is independent of


If A lies in second quadrant 3tan A + 4 = 0, then the value of 2cot A − 5cosA + sin A is equal to


If sec x + tan x = k, cos x =


The value of \[\cos1^\circ \cos2^\circ \cos3^\circ . . . \cos179^\circ\] is

 

Find the general solution of the following equation:

\[\sin x = \frac{1}{2}\]

Find the general solution of the following equation:

\[\cos x = - \frac{\sqrt{3}}{2}\]

If cos x = k has exactly one solution in [0, 2π], then write the values(s) of k.

 

A solution of the equation \[\cos^2 x + \sin x + 1 = 0\], lies in the interval


The number of values of ​x in [0, 2π] that satisfy the equation \[\sin^2 x - \cos x = \frac{1}{4}\]


The equation \[3 \cos x + 4 \sin x = 6\] has .... solution.


Find the principal solution and general solution of the following:
sin θ = `-1/sqrt(2)`


Solve the following equations:
cot θ + cosec θ = `sqrt(3)`


Choose the correct alternative:
If cos pθ + cos qθ = 0 and if p ≠ q, then θ is equal to (n is any integer)


Choose the correct alternative:
If sin α + cos α = b, then sin 2α is equal to


Number of solutions of the equation tan x + sec x = 2 cosx lying in the interval [0, 2π] is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×