English Medium इयत्ता १० - CBSE Question Bank Solutions

`sin^2 theta + cos^4 theta = cos^2 theta + sin^4 theta`

cosec⁴ θ − cosec² θ = cot⁴ θ + cot² θ

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

`(1-tan^2 theta)/(cot^2-1) = tan^2 theta`

`(tan theta)/((sec theta -1))+(tan theta)/((sec theta +1)) = 2 sec theta`

`(cot ^theta)/((cosec theta+1)) + ((cosec theta + 1))/cot theta = 2 sec theta`

`cot theta/((cosec  theta + 1) )+ ((cosec  theta +1 ))/ cot theta = 2 sec theta `

`(sec theta -1 )/( sec theta +1) = ( sin ^2 theta)/( (1+ cos theta )^2)`

`(sectheta- tan theta)/(sec theta + tan theta) = ( cos ^2 theta)/( (1+ sin theta)^2)`

`sqrt((1 + sin θ)/(1 - sin θ)) = sec θ + tan θ`

`sqrt((1-cos theta)/(1+cos theta)) = (cosec  theta - cot  theta)`

`sqrt((1+cos theta)/(1-cos theta)) + sqrt((1-cos theta )/(1+ cos theta )) = 2 cosec theta`

`(cos^3 θ + sin^3 θ)/(cos θ + sin θ) + (cos ^3 θ - sin^3 θ)/(cos θ - sin θ) = 2`

Prove the following identities:

`sin theta/((cot theta + "cosec"  theta)) - sin theta/((cot theta - "cosec"  theta)) = 2`

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

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

Prove the following identities:

`(1 + cos theta - sin^2 theta )/(sin theta (1 + cos theta)) = cot theta`

Prove the following identities:

`("cosec"  theta + cot theta)/("cosec"  theta - cot theta) = ("cosec"  theta + cot theta )^2 = 1 + 2 cot^2 theta + 2  "cosec"  theta cot theta`

Prove the following identities:

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

Prove the following identities:

`(1 + cos theta + sin theta)/(1 + cos theta - sin theta) = (1 + sin theta )/(cos theta)`