Advertisements
Advertisements
Question
Prove the following identity :
`1/(sinA + cosA) + 1/(sinA - cosA) = (2sinA)/(1 - 2cos^2A)`
Advertisements
Solution
LHS = `1/(sinA + cosA) + 1/(sinA - cosA)`
= `(sinA - cosA + sinA + cosA)/(sin^2A - cos^2A)`
= `(2sinA)/(1 - cos^2A - cos^2A) = (2sinA)/(1 - 2cos^2A)`
APPEARS IN
RELATED QUESTIONS
Prove the following trigonometric identities.
`sqrt((1 - cos theta)/(1 + cos theta)) = cosec theta - cot theta`
Prove the following trigonometric identities.
`sqrt((1 - cos A)/(1 + cos A)) = cosec A - cot A`
If 3 sin θ + 5 cos θ = 5, prove that 5 sin θ – 3 cos θ = ± 3.
If `( cosec theta + cot theta ) =m and ( cosec theta - cot theta ) = n, ` show that mn = 1.
Prove the following identity :
`(cotA - cosecA)^2 = (1 - cosA)/(1 + cosA)`
If sinA + cosA = m and secA + cosecA = n , prove that n(m2 - 1) = 2m
Prove that `sqrt((1 - sin θ)/(1 + sin θ)) = sec θ - tan θ`.
Prove that identity:
`(sec A - 1)/(sec A + 1) = (1 - cos A)/(1 + cos A)`
If 5 sec θ – 12 cosec θ = 0, then find values of sin θ, sec θ.
(1 + sin A)(1 – sin A) is equal to ______.
