HSC Science (General) ११ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

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

Prove the following:

`(tan theta + 1/costheta)^2 + (tan theta - 1/costheta)^2 = 2((1 + sin^2theta)/(1 - sin^2theta))`

Prove the following:

2 sec²θ – sec⁴θ – 2cosec²θ + cosec⁴θ = cot⁴θ – tan⁴θ

Prove the following:

sin⁴θ + cos⁴θ = 1 – 2 sin²θ cos²θ

Prove the following:

2(sin⁶θ + cos⁶θ) – 3(sin⁴θ + cos⁴θ) + 1 = 0

Prove the following:

cos⁴θ − sin⁴θ +1= 2cos²θ

Prove the following:

sin⁴θ +2sin²θ . cos²θ = 1 − cos⁴θ