English Medium इयत्ता १० - CBSE Question Bank Solutions

Given that:
(1 + cos α) (1 + cos β) (1 + cos γ) = (1 − cos α) (1 − cos α) (1 − cos β) (1 − cos γ)

Show that one of the values of each member of this equality is sin α sin β sin γ

If sin θ + cos θ = x, prove that  `sin^6 theta + cos^6 theta = (4- 3(x^2 - 1)^2)/4`

If x = a sec θ cos ϕ, y = b sec θ sin ϕ and z = c tan θ, show that `x^2/a^2 + y^2/b^2 - x^2/c^2 = 1`

(i)` (1-cos^2 theta )cosec^2theta = 1`

`(1 + cot^2 theta ) sin^2 theta =1`

`(sec^2 theta-1) cot ^2 theta=1`

`(sec^2 theta -1)(cosec^2 theta - 1)=1`

`(1-cos^2theta) sec^2 theta = tan^2 theta`

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

`1/((1+tan^2 theta)) + 1/((1+ tan^2 theta))`

`(1+ cos theta)(1- costheta )(1+cos^2 theta)=1`

`cosec theta (1+costheta)(cosectheta - cot theta )=1`

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

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

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

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

`sec theta (1- sin theta )( sec theta + tan theta )=1`

`sin theta (1+ tan theta) + cos theta (1+ cot theta) = ( sectheta+ cosec  theta)`

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

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