Advertisements
Advertisements
प्रश्न
Prove that `cot^2 pi/6 + cosec (5pi)/6 + 3 tan^2 pi/6 = 6`
उत्तर
Left side = `cot^2 pi/6 + cosec (5pi)/6 + 3 tan^2 pi/6`
= `(sqrt3)^2 + cosec (pi-pi/6) + 3 (1/sqrt3)^2`
`(∴ cot pi/6 = sqrt3, tan pi/6 = 1/sqrt3)`
= 3 + cosec `pi/6+ 3 xx 1/3`
[∵cosec `(pi-θ)= cosec θ`]
= 3 + 2 + 1 = 6 = Right Side.
APPEARS IN
संबंधित प्रश्न
Find the value of: sin 75°
Prove the following:
`(sin x - sin 3x)/(sin^2 x - cos^2 x) = 2sin x`
Prove the following:
`(cos 4x + cos 3x + cos 2x)/(sin 4x + sin 3x + sin 2x) = cot 3x`
Prove the following:
`tan 4x = (4tan x(1 - tan^2 x))/(1 - 6tan^2 x + tan^4 x)`
Prove the following:
cos 6x = 32 cos6 x – 48 cos4 x + 18 cos2 x – 1
If \[\sin A = \frac{1}{2}, \cos B = \frac{\sqrt{3}}{2}\], where \[\frac{\pi}{2}\] < A < π and 0 < B < \[\frac{\pi}{2}\], find the following:
tan (A + B)
Evaluate the following:
sin 78° cos 18° − cos 78° sin 18°
Prove that
\[\frac{\tan A + \tan B}{\tan A - \tan B} = \frac{\sin \left( A + B \right)}{\sin \left( A - B \right)}\]
Prove that:
Prove that:
\[\cos^2 45^\circ - \sin^2 15^\circ = \frac{\sqrt{3}}{4}\]
Prove that:
sin2 (n + 1) A − sin2 nA = sin (2n + 1) A sin A.
Prove that:
\[\frac{\tan^2 2x - \tan^2 x}{1 - \tan^2 2x \tan^2 x} = \tan 3x \tan x\]
If sin α + sin β = a and cos α + cos β = b, show that
Prove that:
Prove that:
Reduce each of the following expressions to the sine and cosine of a single expression:
\[\sqrt{3} \sin x - \cos x\]
Reduce each of the following expressions to the sine and cosine of a single expression:
cos x − sin x
Write the maximum value of 12 sin x − 9 sin2 x.
If 12 sin x − 9sin2 x attains its maximum value at x = α, then write the value of sin α.
If a = b \[\cos \frac{2\pi}{3} = c \cos\frac{4\pi}{3}\] then write the value of ab + bc + ca.
If A + B = C, then write the value of tan A tan B tan C.
If A + B + C = π, then sec A (cos B cos C − sin B sin C) is equal to
If \[\tan A = \frac{a}{a + 1}\text{ and } \tan B = \frac{1}{2a + 1}\]
If 3 sin x + 4 cos x = 5, then 4 sin x − 3 cos x =
If cot (α + β) = 0, sin (α + 2β) is equal to
If tan θ1 tan θ2 = k, then \[\frac{\cos \left( \theta_1 - \theta_2 \right)}{\cos \left( \theta_1 + \theta_2 \right)} =\]
If A − B = π/4, then (1 + tan A) (1 − tan B) is equal to
The maximum value of \[\sin^2 \left( \frac{2\pi}{3} + x \right) + \sin^2 \left( \frac{2\pi}{3} - x \right)\] is
If tan 69° + tan 66° − tan 69° tan 66° = 2k, then k =
If \[\tan\alpha = \frac{x}{x + 1}\] and \[\tan\alpha = \frac{x}{x + 1}\], then \[\alpha + \beta\] is equal to
Express the following as the sum or difference of sines and cosines:
2 sin 3x cos x
Express the following as the sum or difference of sines and cosines:
2 sin 4x sin 3x
If `(sin(x + y))/(sin(x - y)) = (a + b)/(a - b)`, then show that `tanx/tany = a/b` [Hint: Use Componendo and Dividendo].
If sin(θ + α) = a and sin(θ + β) = b, then prove that cos 2(α - β) - 4ab cos(α - β) = 1 - 2a2 - 2b2
[Hint: Express cos(α - β) = cos((θ + α) - (θ + β))]
If sinθ + cosecθ = 2, then sin2θ + cosec2θ is equal to ______.
If tanA = `1/2`, tanB = `1/3`, then tan(2A + B) is equal to ______.
If α + β = `pi/4`, then the value of (1 + tan α)(1 + tan β) is ______.
If sinx + cosx = a, then |sinx – cosx| = ______.
