Advertisements
Advertisements
प्रश्न
`(cos theta cosec theta - sin theta sec theta )/(costheta + sin theta) = cosec theta - sec theta`
Advertisements
उत्तर
LHS = `(cos theta cosec theta - sin theta sec theta )/(costheta + sin theta)`
=`((cos theta sin theta)/(sin theta cos theta))/(cos theta + sin theta)`
=`(cos^2 theta - sin^2 theta)/(cos theta sin theta ( cos theta + sin theta))`
=`((cos theta + sin theta )( cos theta - sin theta))/(cos theta sin theta ( cos theta + sin theta))`
=`((cos theta - sin theta ))/(cos theta sin theta)`
=`1/ sin theta - 1/ cos theta`
=`cosec theta - sec theta`
= RHS
Hence, LHS = RHS
APPEARS IN
संबंधित 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`
Prove the following identities:
`1/(1 - sinA) + 1/(1 + sinA) = 2sec^2A`
Prove the following identities:
`1/(sinA + cosA) + 1/(sinA - cosA) = (2sinA)/(1 - 2cos^2A)`
Prove that:
`(sinA - sinB)/(cosA + cosB) + (cosA - cosB)/(sinA + sinB) = 0`
Find the value of sin ` 48° sec 42° + cos 48° cosec 42°`
If `sec theta = x ,"write the value of tan" theta`.
If x = a cos θ and y = b sin θ, then b2x2 + a2y2 =
Prove the following identity :
`(1 - sin^2θ)sec^2θ = 1`
Prove the following identity :
secA(1 - sinA)(secA + tanA) = 1
Prove the following identity :
`1/(tanA + cotA) = sinAcosA`
Prove the following identity :
`(cosecθ)/(tanθ + cotθ) = cosθ`
Prove that `cos θ/sin(90° - θ) + sin θ/cos (90° - θ) = 2`.
Prove that: `cos^2 A + 1/(1 + cot^2 A) = 1`.
Prove that: `(1 + cot^2 θ/(1 + cosec θ)) = cosec θ`.
Prove the following identities.
(sin θ + sec θ)2 + (cos θ + cosec θ)2 = 1 + (sec θ + cosec θ)2
Prove that cot2θ – tan2θ = cosec2θ – sec2θ
Prove that 2(sin6A + cos6A) – 3(sin4A + cos4A) + 1 = 0
If 3 sin A + 5 cos A = 5, then show that 5 sin A – 3 cos A = ± 3
`sqrt((1 - cos^2theta) sec^2 theta) = tan theta`
Given that sinθ + 2cosθ = 1, then prove that 2sinθ – cosθ = 2.
