Advertisements
Advertisements
Question
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`sqrt((1+sinA)/(1-sinA)) = secA + tanA`
Advertisements
Solution
L.H.S
= `sqrt((1+sinA)/(1-sinA))`
= `sqrt(((1+sinA)(1+sinA))/((1-sinA)(1+sinA))`
= `(1+sinA)/(sqrt(1-sin^2A))`
= `(1+sinA)/sqrt(cos^2A)`
= `(1+sinA)/cosA`
= secA + tan A
= `1/cos A + sin A/cos A`
= R.H.S
APPEARS IN
RELATED QUESTIONS
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`cos A/(1 + sin A) + (1 + sin A)/cos A = 2 sec A`
Prove the following trigonometric identities.
`sqrt((1 - cos theta)/(1 + cos theta)) = cosec theta - cot theta`
Prove the following trigonometric identities.
`1/(sec A - 1) + 1/(sec A + 1) = 2 cosec A cot A`
If a cos θ + b sin θ = m and a sin θ – b cos θ = n, prove that a2 + b2 = m2 + n2
Prove the following identities:
`(secA - tanA)/(secA + tanA) = 1 - 2secAtanA + 2tan^2A`
If x = a cos θ and y = b cot θ, show that:
`a^2/x^2 - b^2/y^2 = 1`
Prove that:
`1/(sinA - cosA) - 1/(sinA + cosA) = (2cosA)/(2sin^2A - 1)`
`sin theta (1+ tan theta) + cos theta (1+ cot theta) = ( sectheta+ cosec theta)`
`((sin A- sin B ))/(( cos A + cos B ))+ (( cos A - cos B ))/(( sinA + sin B ))=0`
Show that none of the following is an identity:
`sin^2 theta + sin theta =2`
If `sin theta = x , " write the value of cot "theta .`
Prove that:
`"tanθ"/("secθ" – 1) = (tanθ + secθ + 1)/(tanθ + secθ - 1)`
If a cot θ + b cosec θ = p and b cot θ − a cosec θ = q, then p2 − q2
If x = acosθ , y = bcotθ , prove that `a^2/x^2 - b^2/y^2 = 1.`
Evaluate:
`(tan 65°)/(cot 25°)`
If sec θ = x + `1/(4"x"), x ≠ 0,` find (sec θ + tan θ)
Prove that ( 1 + tan A)2 + (1 - tan A)2 = 2 sec2A
Prove that `costheta/(1 + sintheta) = (1 - sintheta)/(costheta)`
Show that tan4θ + tan2θ = sec4θ – sec2θ.
(1 + sin A)(1 – sin A) is equal to ______.
