Advertisements
Advertisements
Question
Prove the following identity :
secA(1 - sinA)(secA + tanA) = 1
Advertisements
Solution
LHS = secA(1 - sinA)(secA + tanA)
= `1/cosA(1-sinA)(1/cosA + sinA/cosA)`
= `((1 -sinA))/cosA((1 + sinA)/cosA) = ((1 - sin^2A)/cos^2A)`
= `(cos^2A/cos^2A)`
= 1 = RHS
APPEARS IN
RELATED QUESTIONS
Prove the following trigonometric identities.
`tan theta + 1/tan theta` = sec θ.cosec θ
Prove the following trigonometric identities
`((1 + sin theta)^2 + (1 + sin theta)^2)/(2cos^2 theta) = (1 + sin^2 theta)/(1 - sin^2 theta)`
Prove the following trigonometric identities.
`sqrt((1 - cos A)/(1 + cos A)) = cosec A - cot A`
If m = a sec A + b tan A and n = a tan A + b sec A, then prove that : m2 – n2 = a2 – b2
`cos^2 theta /((1 tan theta))+ sin ^3 theta/((sin theta - cos theta))=(1+sin theta cos theta)`
Write the value of `( 1- sin ^2 theta ) sec^2 theta.`
Eliminate θ, if
x = 3 cosec θ + 4 cot θ
y = 4 cosec θ – 3 cot θ
Prove the following identity :
`1/(sinA + cosA) + 1/(sinA - cosA) = (2sinA)/(1 - 2cos^2A)`
Prove that sin2A . tan A + cos2A . cot A + 2 sin A . cos A = tan A + cot A.
If cosec θ + cot θ = p, then prove that cos θ = `(p^2 - 1)/(p^2 + 1)`
