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

Evaluate the following:

sin 30° + cos 45° + tan 180°

Evaluate the following : 

cosec 45° + cot 45° + tan 0°

Evaluate the following : 

sin 30° × cos 45° × tan 360°

If tanθ = `1/2`, evaluate `(2sin theta + 3cos theta)/(4cos theta + 3sin theta)`

Eliminate θ from the following: 

x = 3secθ , y = 4tanθ

Eliminate θ from the following : 

x = 6cosecθ, y = 8cotθ

Eliminate θ from the following :

x = 4cosθ − 5sinθ, y = 4sinθ + 5cosθ

Eliminate θ from the following :

x = 5 + 6cosecθ, y = 3 + 8cotθ

Eliminate θ from the following:

2x = 3 − 4 tan θ, 3y = 5 + 3 sec θ

Find the acute angle θ such that 2 cos²θ = 3 sin θ.

Find the acute angle θ such that 5tan²θ + 3 = 9secθ.

Find sinθ such that 3cosθ + 4sinθ = 4

If cosecθ + cotθ = 5, then evaluate secθ.

If cotθ = `3/4` and π < θ < `(3pi)/2` then find the value of 4cosecθ + 5cosθ.

Prove the following identities:

`(1 + tan^2 "A") + (1 + 1/tan^2"A") = 1/(sin^2 "A" - sin^4"A")`

Prove the following identities: 

(cos²A – 1) (cot²A + 1) = −1

Prove the following identities:

(sinθ + sec θ)² + (cosθ + cosec θ)² = (1 + cosecθ sec θ)² 

Prove the following identities:

(1 + cot θ – cosec θ)(1 + tan θ + sec θ) = 2

Prove the following identities:

`tan^3theta/(1 + tan^2theta) + cot^3theta/(1 + cot^2theta` = secθ cosecθ – 2sinθ cosθ

Prove the following identities:

`1/(sectheta + tantheta) - 1/costheta = 1/costheta - 1/(sectheta - tantheta)`