Advertisements
Advertisements
प्रश्न
Prove that `(sec A)/(tan A + cot A) = sin A`.
Advertisements
उत्तर
L.H.S. = `(sec A)/(tan A + cot A)`
= `(sec A)/((sin A)/(cos A) + (cos A)/(sin A))`
= `(sec A)/((sin^2A + cos^2A)/(cosA sinA))`
= `(sec A)/(1/(cosA sinA))` ...[∵ sin2A + cos2A = 1]
= sec A cos A sin A
= `1/(cos A) xx cos A sin A`
= sin A
= R.H.S.
∴ `(sec A)/(tan A + cot A) = sin A`
संबंधित प्रश्न
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(sin theta-2sin^3theta)/(2cos^3theta -costheta) = tan theta`
Prove the following trigonometric identity:
`sqrt((1 + sin A)/(1 - sin A)) = sec A + tan A`
Prove the following trigonometric identities.
`(1 + tan^2 A) + (1 + 1/tan^2 A) = 1/(sin^2 A - sin^4 A)`
Prove the following trigonometric identities.
tan2 A sec2 B − sec2 A tan2 B = tan2 A − tan2 B
`sin theta/((cot theta + cosec theta)) - sin theta /( (cot theta - cosec theta)) =2`
`(tan A + tanB )/(cot A + cot B) = tan A tan B`
Write the value of `( 1- sin ^2 theta ) sec^2 theta.`
Simplify : 2 sin30 + 3 tan45.
Prove the following identity :
secA(1 + sinA)(secA - tanA) = 1
Prove the following identity :
`sin^2Acos^2B - cos^2Asin^2B = sin^2A - sin^2B`
Prove the following identity :
`sec^2A.cosec^2A = tan^2A + cot^2A + 2`
Prove the following identity :
`cosecA + cotA = 1/(cosecA - cotA)`
Prove the following identity :
`(cosecθ)/(tanθ + cotθ) = cosθ`
Prove that: 2(sin6θ + cos6θ) - 3 ( sin4θ + cos4θ) + 1 = 0.
If sin θ + sin2 θ = 1 show that: cos2 θ + cos4 θ = 1
cot θ . tan θ = ?
Prove that `"cosec" θ xx sqrt(1 - cos^2θ) = 1`.
Prove that cos2θ . (1 + tan2θ) = 1. Complete the activity given below.
Activity:
L.H.S. = `square`
= `cos^2θ xx square` ...`[1 + tan^2θ = square]`
= `(cos θ xx square)^2`
= 12
= 1
= R.H.S.
If cosA + cos2A = 1, then sin2A + sin4A = 1.
If sinθ = `11/61`, then find the value of cosθ using the trigonometric identity.
