English Medium इयत्ता १० - CBSE Question Bank Solutions for Mathematics

If `( tan theta + sin theta ) = m and ( tan theta - sin theta ) = n " prove that "(m^2-n^2)^2 = 16 mn .`

If `(cot theta ) = m and ( sec theta - cos theta) = n " prove that " (m^2 n)(2/3) - (mn^2)(2/3)=1`

If `(cosec theta - sin theta )= a^3 and (sec theta - cos theta ) = b^3 , " prove that " a^2 b^2 ( a^2+ b^2 ) =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 theta - sin theta ) and n = ( cos theta +  sin theta ) "then show that" sqrt(m/n) + sqrt(n/m) = 2/sqrt(1-tan^2 theta)`.

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).`