Advertisements
Advertisements
प्रश्न
` (sin theta - cos theta) / ( sin theta + cos theta ) + ( sin theta + cos theta ) / ( sin theta - cos theta ) = 2/ ((2 sin^2 theta -1))`
Advertisements
उत्तर
LHS = `(sin theta - cos theta )/ (sin theta + cos theta) +( sin theta + cos theta )/( sin theta - cos theta )`
=` ((sin theta - cos theta )^2 + (( sin theta + cos theta )^2))/((sin theta + cos theta )( sin theta - cos theta ))`
=` (sin^2 theta + cos ^2 theta -2 sin theta cos theta + sin^2 theta + cos^2 theta + 2 sin theta cos theta)/( sin^ 2theta - cos^ 2theta)`
=` (1+1)/(sin^2 theta - ( 1-sin ^2 theta)) ( ∵ sin^2 theta + cos^2 theta =1)`
=`2/(sin^2 theta - 1 + sin^2 theta)`
=` 2/ (sin^2 theta -1)`
= RHS
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`(cos^2 theta)/sin theta - cosec theta + sin theta = 0`
Prove the following trigonometric identities.
`cos A/(1 - tan A) + sin A/(1 - cot A) = sin A + cos A`
Prove the following trigonometric identities.
`cot^2 A cosec^2B - cot^2 B cosec^2 A = cot^2 A - cot^2 B`
If sin θ + cos θ = x, prove that `sin^6 theta + cos^6 theta = (4- 3(x^2 - 1)^2)/4`
Prove the following identities:
`(sintheta - 2sin^3theta)/(2cos^3theta - costheta) = tantheta`
Prove the following identities:
`((cosecA - cotA)^2 + 1)/(secA(cosecA - cotA)) = 2cotA`
`(1-cos^2theta) sec^2 theta = tan^2 theta`
Define an identity.
The value of (1 + cot θ − cosec θ) (1 + tan θ + sec θ) is
Prove the following identity :
( 1 + cotθ - cosecθ) ( 1 + tanθ + secθ)
Prove the following identity :
`cosec^4A - cosec^2A = cot^4A + cot^2A`
Prove the following identities:
`(sec"A"-1)/(sec"A"+1)=(sin"A"/(1+cos"A"))^2`
Prove the following identity :
`(sinA + cosA)/(sinA - cosA) + (sinA - cosA)/(sinA + cosA) = 2/(2sin^2A - 1)`
Given `cos38^circ sec(90^circ - 2A) = 1` , Find the value of <A
Evaluate:
`(tan 65°)/(cot 25°)`
Prove the following identities.
tan4 θ + tan2 θ = sec4 θ – sec2 θ
Prove the following identities.
`sqrt((1 + sin theta)/(1 - sin theta)` = sec θ + tan θ
Show that `(cos^2(45^circ + θ) + cos^2(45^circ - θ))/(tan(60^circ + θ) tan(30^circ - θ)) = 1`
Eliminate θ if x = r cosθ and y = r sinθ.
