Advertisements
Advertisements
Question
Prove that `(sin theta)/(1-cottheta) + (cos theta)/(1 - tan theta) = cos theta + sin theta`
Advertisements
Solution
L.H.S = `(sin theta)/(1 - cot theta) + (cos theta)/(1- tan theta)`
`= (sin theta)/(1 - cos theta/sin theta) + cos theta/(1 - sin theta/cos theta)`
`= sin^2 theta/(sin theta - cos theta) + cos^2 theta/(cos theta - sin theta)`
`= (sin^2 theta)/(sin theta - cos theta) - cos^2 theta/(sin theta - costheta)`
`= (sin^2 theta - cos^2 theta)/(sin theta - cos theta)`
`= ((sin theta - cos theta)(sin theta + cos theta))/(sin theta - cos theta)`
`= sin theta + cos theta`
= R.H.S
APPEARS IN
RELATED QUESTIONS
Prove the following trigonometric identities:
`(\text{i})\text{ }\frac{\sin \theta }{1-\cos \theta }=\text{cosec}\theta+\cot \theta `
Prove the following trigonometric identities.
(sec2 θ − 1) (cosec2 θ − 1) = 1
Prove the following trigonometric identities.
`sqrt((1 - cos A)/(1 + cos A)) = cosec A - cot A`
Prove the following identities:
cosec A(1 + cos A) (cosec A – cot A) = 1
Prove that:
cos A (1 + cot A) + sin A (1 + tan A) = sec A + cosec A
`1 + (tan^2 θ)/((1 + sec θ)) = sec θ`
Prove the following identities.
`(1 - tan^2theta)/(cot^2 theta - 1)` = tan2 θ
Prove that `(cos(90^circ - A))/(sin A) = (sin(90^circ - A))/(cos A)`.
If tan α + cot α = 2, then tan20α + cot20α = ______.
(1 + sin A)(1 – sin A) is equal to ______.
