Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
If sinθ + cosθ = p and secθ + cosecθ = q, show that q(p2 – 1) = 2p
(secA + tanA) (1 − sinA) = ______.
Prove that `sqrt((1 + cos theta)/(1 - cos theta)) + sqrt((1 - cos theta)/(1 + cos theta)) = 2 cosec theta`
Prove the following identities:
`cot^2A/(cosecA + 1)^2 = (1 - sinA)/(1 + sinA)`
If x = r cos A cos B, y = r cos A sin B and z = r sin A, show that : x2 + y2 + z2 = r2
Prove the following identities:
(1 + tan A + sec A) (1 + cot A – cosec A) = 2
`(sec^2 theta -1)(cosec^2 theta - 1)=1`
`1/((1+ sin θ)) + 1/((1 - sin θ)) = 2 sec^2 θ`
`1 + (tan^2 θ)/((1 + sec θ)) = sec θ`
What is the value of (1 − cos2 θ) cosec2 θ?
What is the value of \[\sin^2 \theta + \frac{1}{1 + \tan^2 \theta}\]
Without using trigonometric table , evaluate :
`cos90^circ + sin30^circ tan45^circ cos^2 45^circ`
Find A if tan 2A = cot (A-24°).
Prove that:
`(sin A + cos A)/(sin A - cos A) + (sin A - cos A)/(sin A + cos A) = 2/(2 sin^2 A - 1)`
Prove that `(tan^2 theta - 1)/(tan^2 theta + 1)` = 1 – 2 cos2θ
Prove that 2(sin6A + cos6A) – 3(sin4A + cos4A) + 1 = 0
Prove that (1 – cos2A) . sec2B + tan2B(1 – sin2A) = sin2A + tan2B
If 4 tanβ = 3, then `(4sinbeta-3cosbeta)/(4sinbeta+3cosbeta)=` ______.
Simplify (1 + tan2θ)(1 – sinθ)(1 + sinθ)
Complete the following activity to prove:
cotθ + tanθ = cosecθ × secθ
Activity: L.H.S. = cotθ + tanθ
= `cosθ/sinθ + square/cosθ`
= `(square + sin^2theta)/(sinθ xx cosθ)`
= `1/(sinθ xx cosθ)` ....... ∵ `square`
= `1/sinθ xx 1/cosθ`
= `square xx secθ`
∴ L.H.S. = R.H.S.
