Advertisements
Advertisements
प्रश्न
If sinθ + cosθ = 1, then the value of sin2θ is equal to ______.
विकल्प
1
`1/2`
0
–1
Advertisements
उत्तर
If sinθ + cosθ = 1, then the value of sin2θ is equal to 0.
Explanation:
Given that: sinθ + cosθ = 1
⇒ (sinθ + cosθ)2 = (1)2
⇒ sin2θ + cos2θ + 2sinθ cosθ = 1
⇒ 1 + sin2θ = 1
⇒ sin2θ = 1 – 1 = 0
APPEARS IN
संबंधित प्रश्न
Find the value of: sin 75°
Prove the following:
sin (n + 1)x sin (n + 2)x + cos (n + 1)x cos (n + 2)x = cos x
Prove the following:
sin2 6x – sin2 4x = sin 2x sin 10x
Prove the following:
`(cos9x - cos5x)/(sin17x - sin 3x) = - (sin2x)/(cos 10x)`
Prove the following:
`(sin 5x + sin 3x)/(cos 5x + cos 3x) = tan 4x`
Prove the following:
`(sin x + sin 3x)/(cos x + cos 3x) = tan 2x`
Prove the following:
cos 6x = 32 cos6 x – 48 cos4 x + 18 cos2 x – 1
Prove that: `(cos x + cos y)^2 + (sin x - sin y )^2 = 4 cos^2 (x + y)/2`
If \[\sin A = \frac{4}{5}\] and \[\cos B = \frac{5}{13}\], where 0 < A, \[B < \frac{\pi}{2}\], find the value of the following:
If \[\sin A = \frac{12}{13}\text{ and } \sin B = \frac{4}{5}\], where \[\frac{\pi}{2}\] < A < π and 0 < B < \[\frac{\pi}{2}\], find the following:
cos (A + B)
If \[\cos A = - \frac{24}{25}\text{ and }\cos B = \frac{3}{5}\], where π < A < \[\frac{3\pi}{2}\text{ and }\frac{3\pi}{2}\]< B < 2π, find the following:
cos (A + B)
If \[\tan A = \frac{3}{4}, \cos B = \frac{9}{41}\], where π < A < \[\frac{3\pi}{2}\] and 0 < B <\[\frac{\pi}{2}\], find tan (A + B).
Prove that
\[\frac{\tan A + \tan B}{\tan A - \tan B} = \frac{\sin \left( A + B \right)}{\sin \left( A - B \right)}\]
Prove that \[\frac{\tan 69^\circ + \tan 66^\circ}{1 - \tan 69^\circ \tan 66^\circ} = - 1\].
Prove that:
\[\frac{\sin \left( A - B \right)}{\cos A \cos B} + \frac{\sin \left( B - C \right)}{\cos B \cos C} + \frac{\sin \left( C - A \right)}{\cos C \cos A} = 0\]
Prove that:
cos2 A + cos2 B − 2 cos A cos B cos (A + B) = sin2 (A + B)
Prove that:
tan 8x − tan 6x − tan 2x = tan 8x tan 6x tan 2x
Prove that:
tan 13x − tan 9x − tan 4x = tan 13x tan 9x tan 4x
If α, β are two different values of x lying between 0 and 2π, which satisfy the equation 6 cos x + 8 sin x = 9, find the value of sin (α + β).
Prove that:
\[\frac{1}{\sin \left( x - a \right) \sin \left( x - b \right)} = \frac{\cot \left( x - a \right) - \cot \left( x - b \right)}{\sin \left( a - b \right)}\]
Prove that:
Prove that:
If α and β are two solutions of the equation a tan x + b sec x = c, then find the values of sin (α + β) and cos (α + β).
Write the interval in which the value of 5 cos x + 3 cos \[\left( x + \frac{\pi}{3} \right) + 3\] lies.
If sin α − sin β = a and cos α + cos β = b, then write the value of cos (α + β).
tan 20° + tan 40° + \[\sqrt{3}\] tan 20° tan 40° is equal to
If 3 sin x + 4 cos x = 5, then 4 sin x − 3 cos x =
tan 3A − tan 2A − tan A =
The value of \[\cos^2 \left( \frac{\pi}{6} + x \right) - \sin^2 \left( \frac{\pi}{6} - x \right)\] is
If tan (π/4 + x) + tan (π/4 − x) = a, then tan2 (π/4 + x) + tan2 (π/4 − x) =
The maximum value of \[\sin^2 \left( \frac{2\pi}{3} + x \right) + \sin^2 \left( \frac{2\pi}{3} - x \right)\] is
If α and β are the solutions of the equation a tan θ + b sec θ = c, then show that tan (α + β) = `(2ac)/(a^2 - c^2)`.
If cotθ + tanθ = 2cosecθ, then find the general value of θ.
Find the general solution of the equation `(sqrt(3) - 1) costheta + (sqrt(3) + 1) sin theta` = 2
[Hint: Put `sqrt(3) - 1` = r sinα, `sqrt(3) + 1` = r cosα which gives tanα = `tan(pi/4 - pi/6)` α = `pi/12`]
The value of tan 75° - cot 75° is equal to ______.
If tanα = `1/7`, tanβ = `1/3`, then cos2α is equal to ______.
Given x > 0, the values of f(x) = `-3cos sqrt(3 + x + x^2)` lie in the interval ______.
State whether the statement is True or False? Also give justification.
If tan(π cosθ) = cot(π sinθ), then `cos(theta - pi/4) = +- 1/(2sqrt(2))`.
