Advertisements
Advertisements
Question
Prove that (cosec A – sin A)(sec A – cos A) sec2 A = tan A.
Advertisements
Solution
L.H.S = `(cosec A - sin A)(secA - cosA)sec^2A`
`= (1/sinA - sinA)(1/cosA - cosA)(1/cos^2A)`
`= ((1 - sin^2A)/sin A)((1- cos^2A)/cos A)(1/(cos^2A))`
`= cos^2A/sinA . sin^2A/cos A . 1/cos^2A`
`= sinA/cosA`
= tan A
= R.H.S
APPEARS IN
RELATED QUESTIONS
Prove that:
sec2θ + cosec2θ = sec2θ x cosec2θ
Prove the following identities:
`cosecA - cotA = sinA/(1 + cosA)`
` (sin theta + cos theta )/(sin theta - cos theta ) + ( sin theta - cos theta )/( sin theta + cos theta) = 2/ ((1- 2 cos^2 theta))`
(sec A + tan A) (1 − sin A) = ______.
Prove the following identity :
`(secA - 1)/(secA + 1) = sin^2A/(1 + cosA)^2`
If sinA + cosA = m and secA + cosecA = n , prove that n(m2 - 1) = 2m
Prove that tan2Φ + cot2Φ + 2 = sec2Φ.cosec2Φ.
Prove that sin( 90° - θ ) sin θ cot θ = cos2θ.
Prove that `(tan θ + sin θ)/(tan θ - sin θ) = (sec θ + 1)/(sec θ - 1)`
If 2sin2θ – cos2θ = 2, then find the value of θ.
