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

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

Select the correct option from the given alternatives:

If θ = 60°, then `(1 + tan^2theta)/(2tantheta)` is equal to

Select the correct option from the given alternatives:

If cosecθ + cotθ = `5/2`, then the value of tanθ is

Select the correct option from the given alternatives:

`1 - sin^2theta/(1 + costheta) + (1 + costheta)/sintheta - sintheta/(1 - costheta)` equals

Select the correct option from the given alternatives:

If cosecθ − cotθ = q, then the value of cot θ is

Select the correct option from the given alternatives:

The value of tan1°.tan2°tan3°..... tan89° is equal to

Prove the following:  

sin²A cos²B + cos²A sin²B + cos²A cos²B + sin²A sin²B = 1

Prove the following:

`((1 + cot theta + tan theta)(sin theta - costheta)) /(sec^3theta - "cosec"^3theta)`= sin²θ cos²θ