Advertisements
Advertisements
प्रश्न
Show that: `tan "A"/(1 + tan^2 "A")^2 + cot "A"/(1 + cot^2 "A")^2 = sin"A" xx cos"A"`
उत्तर
Proof: L.H.S. = `tan"A"/(1 + tan^2 "A")^2 + cot"A"/(1 + cot^2 "A")^2`
= `tan "A"/(sec^2"A")^2 + cot "A"/("cosec"^2"A")^2` ......`[(∵ 1 + cot^2θ = "cosec"^2θ),(1 + tan^2θ = sec^2θ)]`
= `tan "A"/sec^4"A" + cot "A"/("cosec"^4"A")`
= `sin "A"/cos "A" xx 1/(sec^4 "A") + cos "A"/sin "A" xx 1/("cosec"^4 "A")`
= `sin "A"/cos "A" xx cos^4"A" + cos "A"/sin "A" xx sin^4"A"`
= sinA × cos3A + cosA × sin3A
= sinA cosA (cos2A + sin2A)
= sinA cosA (1) ......[∵ cos2A + sin2A = 1]
= sinA.cosA
= R.H.S
L.H.S. = R.H.S.
Hence proved.
APPEARS IN
संबंधित प्रश्न
`(1+tan^2A)/(1+cot^2A)` = ______.
Prove the following trigonometric identities.
`tan A/(1 + tan^2 A)^2 + cot A/((1 + cot^2 A)) = sin A cos A`
Prove the following identities:
(sec A – cos A) (sec A + cos A) = sin2 A + tan2 A
Prove the following identities:
`(cosecA)/(cosecA - 1) + (cosecA)/(cosecA + 1) = 2sec^2A`
Prove that:
`(cos^3A + sin^3A)/(cosA + sinA) + (cos^3A - sin^3A)/(cosA - sinA) = 2`
`sin^2 theta + cos^4 theta = cos^2 theta + sin^4 theta`
`(tan A + tanB )/(cot A + cot B) = tan A tan B`
If a cos `theta + b sin theta = m and a sin theta - b cos theta = n , "prove that "( m^2 + n^2 ) = ( a^2 + b^2 )`
If \[sec\theta + tan\theta = x\] then \[tan\theta =\]
9 sec2 A − 9 tan2 A is equal to
\[\frac{1 + \tan^2 A}{1 + \cot^2 A}\]is equal to
Prove the following identity :
`(1 - sin^2θ)sec^2θ = 1`
Prove the following Identities :
`(cosecA)/(cotA+tanA)=cosA`
If x = a sec θ + b tan θ and y = a tan θ + b sec θ prove that x2 - y2 = a2 - b2.
Prove the following identities.
cot θ + tan θ = sec θ cosec θ
If tan θ = 3, then `(4 sin theta - cos theta)/(4 sin theta + cos theta)` is equal to ______.
If 4 tanβ = 3, then `(4sinbeta-3cosbeta)/(4sinbeta+3cosbeta)=` ______.
Given that sin θ = `a/b`, then cos θ is equal to ______.
If sin A = `1/2`, then the value of sec A is ______.
