Advertisements
Advertisements
Question
Prove that `sqrt((1 + sin A)/(1 - sin A))` = sec A + tan A.
Advertisements
Solution
LHS = `sqrt((1 + sin A)/(1 - sin A))`
= `sqrt((1 + sin A)/(1 - sin A) xx (1 + sin A)/(1 + sin A)`
= `sqrt((1 + sin A)^2/(1 - sin^2 A))`
= `sqrt((1 + sin A)^2/cos^2 A)`
= `(1 + sin A)/cos A`
= sec A + tan A = RHS
RELATED QUESTIONS
Express the ratios cos A, tan A and sec A in terms of sin A.
Prove the following trigonometric identities.
`(cot A + tan B)/(cot B + tan A) = cot A tan B`
Prove the following identities:
`(1+ sin A)/(cosec A - cot A) - (1 - sin A)/(cosec A + cot A) = 2(1 + cot A)`
Prove that:
`(cosecA - sinA)(secA - cosA) = 1/(tanA + cotA)`
Show that : `sinAcosA - (sinAcos(90^circ - A)cosA)/sec(90^circ - A) - (cosAsin(90^circ - A)sinA)/(cosec(90^circ - A)) = 0`
Prove the following identities:
`(1 - cosA)/sinA + sinA/(1 - cosA)= 2cosecA`
Prove that:
`cot^2A/(cosecA - 1) - 1 = cosecA`
Prove that:
(cosec A – sin A) (sec A – cos A) sec2 A = tan A
`cot^2 theta - 1/(sin^2 theta ) = -1`a
`1+((tan^2 theta) cot theta)/(cosec^2 theta) = tan theta`
` (sin theta + cos theta )/(sin theta - cos theta ) + ( sin theta - cos theta )/( sin theta + cos theta) = 2/ ((1- 2 cos^2 theta))`
If (cot θ + tan θ) = m and (sec θ – cos θ) = n, prove that `(m^2 n)^(2//3) - (mn^2)^(2//3) = 1`.
If `sqrt(3) sin theta = cos theta and theta ` is an acute angle, find the value of θ .
If a cos θ − b sin θ = c, then a sin θ + b cos θ =
Prove the following identity :
`(sinA + cosA)/(sinA - cosA) + (sinA - cosA)/(sinA + cosA) = 2/(2sin^2A - 1)`
Prove the following identity :
`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (cosA + 1)/sinA`
prove that `1/(1 + cos(90^circ - A)) + 1/(1 - cos(90^circ - A)) = 2cosec^2(90^circ - A)`
If tan A + sin A = m and tan A − sin A = n, then show that `m^2 - n^2 = 4 sqrt (mn)`.
If tan θ + sec θ = l, then prove that sec θ = `(l^2 + 1)/(2l)`.
