Advertisements
Advertisements
प्रश्न
Prove that `(sin theta)/(1-cottheta) + (cos theta)/(1 - tan theta) = cos theta + sin theta`
Advertisements
उत्तर
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
संबंधित प्रश्न
Prove that `cosA/(1+sinA) + tan A = secA`
Prove the following identities:
`1 - cos^2A/(1 + sinA) = sinA`
Prove that:
(sec A − tan A)2 (1 + sin A) = (1 − sin A)
Write the value of ` sin^2 theta cos^2 theta (1+ tan^2 theta ) (1+ cot^2 theta).`
What is the value of (1 + cot2 θ) sin2 θ?
Prove the following identity :
`(secA - 1)/(secA + 1) = sin^2A/(1 + cosA)^2`
Prove that the following identities:
Sec A( 1 + sin A)( sec A - tan A) = 1.
If 1 + sin2α = 3 sinα cosα, then values of cot α are ______.
The value of 2sinθ can be `a + 1/a`, where a is a positive number, and a ≠ 1.
If 2sin2θ – cos2θ = 2, then find the value of θ.
