HSC Science (General) 11th Standard - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

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:

`cosx/(1 + sinx) = (cot(x/2) - 1)/(cot(x/2) + 1)`

Prove the following:

`(tan(theta/2) + cot(theta/2))/(cot(theta/2) - tan(theta/2))` = secθ

Prove the following:

`1/(tan3"A" - tan"A") - 1/(cot3"A" - cot"A")` = cot2A

Prove the following:

cos7° cos14° cos28° cos56° = `sin68^circ/(16cos83^circ)`

Prove the following:

`(sin^2(-160^circ))/(sin^(2)70^circ) + sin(180^circ - theta)/sintheta` = sec²20°

Prove the following:

`(2cos 4x + 1)/(2cosx + 1)` = (2 cos x – 1) (2 cos 2x – 1)

Prove the following:

cos²x + cos²(x + 120°) + cos²(x – 120°) = `3/2`

Prove the following:

2cosec 2x + cosec x = `secx cot(x/2)`

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:

`cos(pi/4 + x) + cos(pi/4 - x) = sqrt(2)cosx`

Prove the following:

`(sin5x - 2sin3x + sinx)/(cos5x - cosx)` = tanx

Prove the following:

sin²6x − sin²4x = sin2x sin10x