Advertisements
Advertisements
Question
Prove the following:
`(sin^2(-160^circ))/(sin^(2)70^circ) + sin(180^circ - theta)/sintheta` = sec220°
Advertisements
Solution
sin(– 160°) = – sin 160°
= – sin(180° – 20°)
= – sin 20°
sin 70° = sin (90° – 20°) = cos 20°
∴ L.H.S. = `(sin^2(-160^circ))/(sin^(2)70^circ) + sin(180^circ - theta)/sintheta`
= `((-sin20^circ)^2)/((cos20^circ)^2) + sintheta/sintheta`
= `(sin^(2)20^circ)/(cos^(2)20^circ) + 1`
= 1 + tan220°
= sec220°
= R.H.S.
APPEARS IN
RELATED QUESTIONS
Prove the following:
tan10° + tan35° + tan10°.tan35° = 1
Prove the following:
`(cot"A"cot4"A" + 1)/(cot"A" cot4"A" - 1) = (cos3"A")/(cos5"A")`
Prove the following:
(sin 3x + sin x)sin x + (cos 3x – cos x) cos x = 0
Prove the following:
(cos x + cos y)2 + (sin x – sin y)2 = `4cos^2 ((x + y))/2`
Prove the following:
(cos x – cos y)2 + (sin x – sin y)2 = `4sin^2 ((x - y))/2`
Prove the following:
tan x + cot x = 2 cosec 2x
Prove the following:
16 sin θ cos θ cos 2θ cos 4θ cos 8θ = sin 16θ
Prove the following:
cos7° cos14° cos28° cos56° = `sin68^circ/(16cos83^circ)`
Prove the following:
`4 cos x. cos(x + pi/3) . cos (x - pi/3)` = cos 3x
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:
The value of `sin pi/14sin (3pi)/14sin (5pi)/14sin (7pi)/14sin (9pi)/14sin (11pi)/14sin (13pi)/14` is ______.
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:
`(sin5x - 2sin3x + sinx)/(cos5x - cosx)` = tanx
Prove the following:
sin26x − sin24x = sin2x sin10x
Prove the following:
cos22x − cos26x = sin4x sin8x
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 ______.
`(1 - tan^2(45^circ - A))/(1 + tan^2(45^circ - A))` is equal to ______.
If `sqrt((1 + cos A)/(1 - cos A)) = x/y`, then the value of tan A is ______.
If cos 2α = `(3 cos 2β - 1)/(3 - cos 2β)`, then tan α is equal to ______.
If tan A and tan B are the roots of x2 – ax + b = 0, then the value of sin2(A + B) 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 ______.
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` = ______.
The value of `sin π/10` is ______.
The value of cos 6x is equal to ______.
The value of sin 3A sin3 A + cos 3A cos3 A is ______.
