Advertisements
Advertisements
Question
Prove the following identity :
`(cosecA - sinA)(secA - cosA)(tanA + cotA) = 1`
Advertisements
Solution
LHS = `(cosecA - sinA)(secA - cosA)(tanA + cotA)`
= `(1/sinA -sinA)(1/cosA - cosA)(tanA + 1/tanA)`
= `((1-sin^2A)/sinA)((1 - cos^2A)/cosA)(sinA/cosA + cosA/sinA)`
= `(cos^2A/sinA)(sin^2A/cosA)((sin^2A + cos^2A)/(sinA.cosA))`
= 1
APPEARS IN
RELATED QUESTIONS
Evaluate
`(sin ^2 63^@ + sin^2 27^@)/(cos^2 17^@+cos^2 73^@)`
Prove the following trigonometric identities.
`cos A/(1 - tan A) + sin A/(1 - cot A) = sin A + cos A`
Prove the following identities:
`1/(sinA + cosA) + 1/(sinA - cosA) = (2sinA)/(1 - 2cos^2A)`
If 3 `cot theta = 4 , "write the value of" ((2 cos theta - sin theta))/(( 4 cos theta - sin theta))`
The value of sin ( \[{45}^° + \theta) - \cos ( {45}^°- \theta)\] is equal to
Prove the following identity :
`sec^2A + cosec^2A = sec^2Acosec^2A`
Prove the following identity :
(secA - cosA)(secA + cosA) = `sin^2A + tan^2A`
Prove the following identity :
`(1 + cosA)/(1 - cosA) = tan^2A/(secA - 1)^2`
Prove the following identities:
`(tan"A"+tan"B")/(cot"A"+cot"B")=tan"A"tan"B"`
Prove that `(sin^2θ)/(cos θ) + cos θ = sec θ`.
