Advertisements
Advertisements
Question
Prove the following identities:
`cot^2A/(cosecA + 1)^2 = (1 - sinA)/(1 + sinA)`
Advertisements
Solution
R.H.S. = `(1 - sinA)/(1 + sinA)`
= `(1 - 1/(cosecA))/(1 + 1/(cosecA))`
= `(cosecA - 1)/(cosecA + 1)`
= `(cosecA - 1)/(cosecA + 1) xx (cosecA + 1)/(cosecA + 1)`
= `(cosec^2A - 1)/(cosecA + 1)^2 = cot^2A/(cosecA + 1)^2` ...(∵ cosec2 A – 1 = cot2 A)
= L.H.S.
APPEARS IN
RELATED QUESTIONS
Prove the following trigonometric identities:
`(1 - cos^2 A) cosec^2 A = 1`
Show that : `sinAcosA - (sinAcos(90^circ - A)cosA)/sec(90^circ - A) - (cosAsin(90^circ - A)sinA)/(cosec(90^circ - A)) = 0`
`costheta/((1-tan theta))+sin^2theta/((cos theta-sintheta))=(cos theta+ sin theta)`
Write the value of `3 cot^2 theta - 3 cosec^2 theta.`
If cosec θ − cot θ = α, write the value of cosec θ + cot α.
If a cos θ + b sin θ = 4 and a sin θ − b sin θ = 3, then a2 + b2 =
If `x/(a cosθ) = y/(b sinθ) "and" (ax)/cosθ - (by)/sinθ = a^2 - b^2 , "prove that" x^2/a^2 + y^2/b^2 = 1`
If tanA + sinA = m and tanA - sinA = n , prove that (`m^2 - n^2)^2` = 16mn
Without using the trigonometric table, prove that
cos 1°cos 2°cos 3° ....cos 180° = 0.
Prove that sec2θ – cos2θ = tan2θ + sin2θ.
