Advertisements
Advertisements
प्रश्न
Prove the following:
(sin 3x + sin x)sin x + (cos 3x – cos x) cos x = 0
उत्तर
L.H.S. = (sin 3x + sin x)sin x + (cos 3x – cos x) cos x
= sin 3x sin x + sin2x + cos 3x cos x – cos2x
= (cos 3x cos x + sin 3x sin x) – (cos2x – sin2x)
= cos (3x – x) – cos 2x
= cos 2x – cos 2x
= 0
= R.H.S.
APPEARS IN
संबंधित प्रश्न
Prove the following:
`(cos27^circ + sin27^circ)/(cos27^circ - sin27^circ)` = tan72°
Prove the following:
tan10° + tan35° + tan10°.tan35° = 1
Prove the following:
(cos x – cos y)2 + (sin x – sin y)2 = `4sin^2 ((x - y))/2`
Prove the following:
16 sin θ cos θ cos 2θ cos 4θ cos 8θ = sin 16θ
Prove the following:
`cosx/(1 + sinx) = (cot(x/2) - 1)/(cot(x/2) + 1)`
Prove the following:
`1/(tan3"A" - tan"A") - 1/(cot3"A" - cot"A")` = cot2A
Prove the following:
`(sin^2(-160^circ))/(sin^(2)70^circ) + sin(180^circ - theta)/sintheta` = sec220°
Prove the following:
`sinx tan(x/2) + 2cosx = 2/(1 + tan^2(x/2))`
Select the correct option from the given alternatives :
The value of cos A cos (60° – A) cos (60° + A) is equal to ......
Select the correct option from the given alternatives :
If α + β + γ = π then the value of sin2α + sin2β – sin2γ is equal to …......
Prove the following:
cot4x (sin5x + sin3x) = cotx (sin5x − sin3x)
Prove the following:
`sqrt(3) "cosec"20^circ - sec20^circ` = 4
`sqrt(3) "cosec" 20^circ - sec 20^circ` is equal to ______.
Let α and β be such that π < α – β < 3π. If sin α + sin β = `- 21/65` and cos α + cos β = `-27/65`, then the value of `cos ((α - β))/2` is ______.
If `x + 1/x` = 2 cos θ, then `x^n + 1/x^n` is equal to ______.
`(1 - tan^2(45^circ - A))/(1 + tan^2(45^circ - A))` is equal to ______.
If sin 4A – cos 2A = cos 4A – sin 2A `("where", 0 < A < π/4)`, then the value of tan 4A is ______.
For any angle θ, the expression `(2 cos 8θ + 1)/(2 cos θ + 1)` is equal to ______.
cot x . cot 2x – cot 2x . cot 3x – cot 3x . cot x is equal to ______.
If tan x = sin 45° cos 45° + sin 30°, then x is equal to ______.
`(sin(90^circ - θ) sin θ)/tanθ + sin^2 θ` is equal to ______.
The value of `(1 + cos π/6)(1 + cos π/3)(1 + cos (2π)/3)(1 + cos (7π)/6)` is equal to ______.
If `tan x + tan(π/3 - x) tan ((2π)/3 + x)` = 3, then ______.
If x sin θ = y cos θ = `(2z tan θ)/(1 - tan^2 θ)`, then 4z2(x2 + y2) is equal to ______.
If sin θ = `12/13, (0 < θ < π/2)` and cos `phi = - 3/5, (π < phi < (3π)/2)`. Then, sin(θ + `phi`) will be ______.
`(sin 3θ - cos 3θ)/(sin θ + cos θ) + 1` = ______.
If tan α = `1/7`, tan β = `1/3`, then cos 2α = ______.
If tan β = cos θ tan α, then `tan^2 θ/2` = ______.
2 sin A cos3 A – 2 sin3 A cos A = ______.
The expression `2 cos π/13. cos (9π)/13 + cos (3π)/13 + cos (5π)/13` is equal to ______.
