Advertisements
Advertisements
प्रश्न
`(sec theta -1 )/( sec theta +1) = ( sin ^2 theta)/( (1+ cos theta )^2)`
Advertisements
उत्तर
LHS = `(sec theta-1)/(sec theta+1)`
=` (1/cos theta-1)/(1/ cos theta +1)`
=`((1-cos theta)/cos theta)/((1+ cos theta)/cos theta)`
=`(1-cos theta)/(1+costheta)`
=`((1-cos theta)(1+ cos theta))/((1+ cos theta)(1+ cos theta)) {"Dividing the numerator and
denominator by "(1+ cos theta)}`
=`(1- cos^2 theta)/((1+ cos theta )^2)`
=`(sin^2 theta)/((1+ cos theta) ^2)`
= RHS
APPEARS IN
संबंधित प्रश्न
Prove the following identities:
`( i)sin^{2}A/cos^{2}A+\cos^{2}A/sin^{2}A=\frac{1}{sin^{2}Acos^{2}A)-2`
`(ii)\frac{cosA}{1tanA}+\sin^{2}A/(sinAcosA)=\sin A\text{}+\cos A`
`( iii)((1+sin\theta )^{2}+(1sin\theta)^{2})/cos^{2}\theta =2( \frac{1+sin^{2}\theta}{1-sin^{2}\theta } )`
If acosθ – bsinθ = c, prove that asinθ + bcosθ = `\pm \sqrt{a^{2}+b^{2}-c^{2}`
(secA + tanA) (1 − sinA) = ______.
Prove the following trigonometric identities.
`sin theta/(1 - cos theta) = cosec theta + cot theta`
Prove that: `sqrt((sec theta - 1)/(sec theta + 1)) + sqrt((sec theta + 1)/(sec theta - 1)) = 2 cosec theta`
If `cosA/cosB = m` and `cosA/sinB = n`, show that : (m2 + n2) cos2 B = n2.
If`( 2 sin theta + 3 cos theta) =2 , " prove that " (3 sin theta - 2 cos theta) = +- 3.`
Find the value of `(cos 38° cosec 52°)/(tan 18° tan 35° tan 60° tan 72° tan 55°)`
If `secθ = 25/7 ` then find tanθ.
Four alternative answers for the following question are given. Choose the correct alternative and write its alphabet:
sin θ × cosec θ = ______
If x = a sec θ and y = b tan θ, then b2x2 − a2y2 =
\[\frac{\tan \theta}{\sec \theta - 1} + \frac{\tan \theta}{\sec \theta + 1}\] is equal to
Prove the following identity :
tanA+cotA=secAcosecA
Prove the following identity :
sinθcotθ + sinθcosecθ = 1 + cosθ
Prove the following identity :
`(1 + tan^2θ)sinθcosθ = tanθ`
Prove that `(sin θ tan θ)/(1 - cos θ) = 1 + sec θ.`
If cosθ + sinθ = `sqrt2` cosθ, show that cosθ - sinθ = `sqrt2` sinθ.
(sec θ + tan θ) . (sec θ – tan θ) = ?
If 5 tan β = 4, then `(5 sin β - 2 cos β)/(5 sin β + 2 cos β)` = ______.
Prove that (sec θ + tan θ) (1 – sin θ) = cos θ
