HSC Arts (English Medium) इयत्ता ११ वी - Maharashtra State Board Question Bank Solutions

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)`

Prove the following identities:

`sintheta/(1 + costheta) + (1 + costheta)/sintheta` = 2cosecθ

Prove the following identity:

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

Prove the following identities:

`cottheta/("cosec"  theta - 1) = ("cosec"  theta + 1)/cot theta`

Prove the following identities:

(sec A + cos A)(sec A − cos A) = tan²A + sin²A

Prove the following identity:

1 + 3cosec²θ cot²θ + cot⁶θ = cosec⁶θ

Prove the following identities:

`(1 - sectheta + tan theta)/(1 + sec theta - tan theta) = (sectheta + tantheta - 1)/(sectheta + tantheta + 1)`

Select the correct option from the given alternatives: 

`tan"A"/(1 + sec"A") + (1 + sec"A")/tan"A"` is equal to