Advertisements
Advertisements
Question
Prove the following identities:
`(sinAtanA)/(1 - cosA) = 1 + secA`
Advertisements
Solution
L.H.S. = `(sinAtanA)/(1 - cosA)`
= `(sinAtanA)/(1 - cosA) xx (1 + cosA)/(1 + cosA)`
= `(sinAtanA(1 + cosA))/(1 - cos^2A)`
= `(sinA sinA/cosA(1 + cosA))/sin^2A`
= `(1 + cosA)/cosA`
= `1/cosA + cosA/cosA`
= sec A + 1
= 1 + sec A = R.H.S.
RELATED QUESTIONS
Prove the following identities:
`(i) cos4^4 A – cos^2 A = sin^4 A – sin^2 A`
`(ii) cot^4 A – 1 = cosec^4 A – 2cosec^2 A`
`(iii) sin^6 A + cos^6 A = 1 – 3sin^2 A cos^2 A.`
9 sec2 A − 9 tan2 A = ______.
Prove the following trigonometric identities.
`sqrt((1 - cos theta)/(1 + cos theta)) = cosec theta - cot theta`
Prove the following trigonometric identities.
(1 + tan2θ) (1 − sinθ) (1 + sinθ) = 1
Prove the following identities:
(cos A + sin A)2 + (cos A – sin A)2 = 2
If sec A + tan A = p, show that:
`sin A = (p^2 - 1)/(p^2 + 1)`
If \[\cos A = \frac{7}{25}\] find the value of tan A + cot A.
(sec A + tan A) (1 − sin A) = ______.
Without using trigonometric identity , show that :
`cos^2 25^circ + cos^2 65^circ = 1`
Prove that sin4A – cos4A = 1 – 2cos2A
