Advertisements
Advertisements
प्रश्न
`(sin theta+1-cos theta)/(cos theta-1+sin theta) = (1+ sin theta)/(cos theta)`
Advertisements
उत्तर
LHS= `(sin theta+1cos theta)/(cos theta-1+sin theta) `
=`((sin theta+1-cos theta)(sin theta+cos theta+1))/((cos theta -1 + sin theta)(sin theta + cos theta +1))`
=`((sin theta + 1 )^2 - cos^2 theta)/((sin theta + cos theta )^2 -1^2)`
=`(sin^2 theta +1+2 sin theta - cos^2 theta)/(sin^2 + cos^2 theta+2 sin theta cos theta -1)`
=`(sin^2 theta + sin^2 theta + cos^2 theta +2sin theta - cos^2 theta)/(2 sin theta cos theta)`
=`(2 sin ^2 theta + 2 sin theta)/(2 sin theta cos theta)`
=`(2 sin theta (1+ sin theta))/(2 sin theta cos theta)`
=`(1+sin theta)/cos theta`
= RHS
APPEARS IN
संबंधित प्रश्न
Prove that `(tan^2 theta)/(sec theta - 1)^2 = (1 + cos theta)/(1 - cos theta)`
If 3 sin θ + 5 cos θ = 5, prove that 5 sin θ – 3 cos θ = ± 3.
Prove the following identities:
sec2A + cosec2A = sec2A . cosec2A
Prove the following identities:
`sqrt((1 - sinA)/(1 + sinA)) = cosA/(1 + sinA)`
`(1-cos^2theta) sec^2 theta = tan^2 theta`
Prove that:
`"tan A"/(1 + "tan"^2 "A")^2 + "Cot A"/(1 + "Cot"^2 "A")^2 = "sin A cos A"`.
If cosec θ − cot θ = α, write the value of cosec θ + cot α.
If cos \[9\theta\] = sin \[\theta\] and \[9\theta\] < 900 , then the value of tan \[6 \theta\] is
Prove the following identity :
(secA - cosA)(secA + cosA) = `sin^2A + tan^2A`
Prove the following identity :
`sec^2A.cosec^2A = tan^2A + cot^2A + 2`
Prove the following identity :
`sec^4A - sec^2A = sin^2A/cos^4A`
Given `cos38^circ sec(90^circ - 2A) = 1` , Find the value of <A
Prove that `sin(90^circ - A).cos(90^circ - A) = tanA/(1 + tan^2A)`
Without using trigonometric identity , show that :
`sin42^circ sec48^circ + cos42^circ cosec48^circ = 2`
Prove that sin θ sin( 90° - θ) - cos θ cos( 90° - θ) = 0
Prove that `cos θ/sin(90° - θ) + sin θ/cos (90° - θ) = 2`.
sec2θ – tan2θ = ?
The value of tan A + sin A = M and tan A - sin A = N.
The value of `("M"^2 - "N"^2) /("MN")^0.5`
Statement 1: sin2θ + cos2θ = 1
Statement 2: cosec2θ + cot2θ = 1
Which of the following is valid?
