English Medium Class 10 - CBSE Question Bank Solutions

If (cot θ + tan θ) = m and (sec θ – cos θ) = n, prove that `(m^2 n)^(2//3) - (mn^2)^(2//3) = 1`.

If (cosec θ – sin θ) = a³ and (sec θ – cos θ) = b³, prove that a²b²(a² + b²) = 1.

If`( 2 sin theta + 3 cos theta) =2 , " prove that " (3 sin theta - 2 cos theta) = +- 3.`

If `( sin theta + cos theta ) = sqrt(2) , " prove that " cot theta = ( sqrt(2)+1)`.

If `( cos theta + sin theta) = sqrt(2) sin theta , " prove that " ( sin theta - cos theta ) = sqrt(2) cos theta`

If `sec theta + tan theta = p,` prove that

(i)`sec theta = 1/2 ( p+1/p)   (ii) tan theta = 1/2 ( p- 1/p) (iii) sin theta = (p^2 -1)/(p^2+1)`

If tan A = n tan B and sin A = m sin B , prove that  `cos^2 A = ((m^2-1))/((n^2 - 1))`

If `m = (cos θ - sin θ)` and `n = (cos θ + sin θ)`, show that `sqrt(m/n) + sqrt(n/m) = 2/sqrt(1 - tan^2θ)`.

Write the value of `( 1- sin ^2 theta  ) sec^2 theta.`

Write the value of `(1 - cos^2 theta ) cosec^2 theta`.

Write the value of `(1 + tan^2 theta ) cos^2 theta`. 

Write the value of `(1 + cot^2 theta ) sin^2 theta`. 

Write the value of `(sin^2 theta 1/(1+tan^2 theta))`. 

Write the value of `(cot^2 theta -  1/(sin^2 theta))`. 

Write the value of `sin theta cos ( 90° - theta )+ cos theta sin ( 90° - theta )`. 

Write the value of ` cosec^2 (90°- theta ) - tan^2 theta`

Write the value of ` sec^2 theta ( 1+ sintheta )(1- sintheta).`

Write the value of `cosec^2 theta (1+ cos theta ) (1- cos theta).`

Write the value of ` sin^2 theta cos^2 theta (1+ tan^2 theta ) (1+ cot^2 theta).`

Write the value of `(1+ tan^2 theta ) ( 1+ sin theta ) ( 1- sin theta)`