Advertisements
Advertisements
प्रश्न
Prove the following identities:
`(1 + tan theta + cot theta)(sin theta - cos theta) = ((sec theta)/("cosec"^2 theta) - ("cosec" theta)/(sec^2 theta))`
Advertisements
उत्तर
LHS = `(1 + tan theta + cot theta )(sintheta - cos theta) `
= `sin theta + tan theta sin theta + cot theta sin theta - cos theta - tan theta cos theta - cot theta cos theta `
= `sin theta + tan theta sin theta + cos theta/sin theta xx sin theta - cos theta - sin theta/cos theta xx cos theta - cot theta cos theta`
= `sin theta + tan theta sin theta + cos theta - cos theta - sin theta - cot theta cos theta`
= `tan theta sin theta - cot theta cos theta`
= `sin theta/cos theta xx 1/(cosec theta) - cos theta/sin theta xx 1/sec theta`
= `1/(cosec theta) xx 1/(cosec theta) xx sec theta - 1/sec theta xx 1/sec theta xx cosec theta`
= `sec theta/(cosec^2 theta) - (cosec theta)/sec^2 theta`
= RHS
Hence, LHS = RHS
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities:
tan2 A + cot2 A = sec2 A cosec2 A − 2
Prove the following trigonometric identities.
if `T_n = sin^n theta + cos^n theta`, prove that `(T_3 - T_5)/T_1 = (T_5 - T_7)/T_3`
Prove the following trigonometric identities.
`(1 + cot A + tan A)(sin A - cos A) = sec A/(cosec^2 A) - (cosec A)/sec^2 A = sin A tan A - cos A cot A`
Prove the following identities:
`(cotA - cosecA)^2 = (1 - cosA)/(1 + cosA)`
Prove the following identities:
`1/(sinA + cosA) + 1/(sinA - cosA) = (2sinA)/(1 - 2cos^2A)`
Prove the following identities:
`((cosecA - cotA)^2 + 1)/(secA(cosecA - cotA)) = 2cotA`
`costheta/((1-tan theta))+sin^2theta/((cos theta-sintheta))=(cos theta+ sin theta)`
Prove the following identities:
`(sin theta + 1 - cos theta)/(cos theta - 1 + sin theta) = (1 + sin theta)/(cos theta)`
If `( sin theta + cos theta ) = sqrt(2) , " prove that " cot theta = ( sqrt(2)+1)`.
If `tan A = 5/12`, find the value of (sin A + cos A) sec A.
Find the value of sin ` 48° sec 42° + cos 48° cosec 42°`
Write True' or False' and justify your answer the following :
The value of \[\cos^2 23 - \sin^2 67\] is positive .
If a cos θ − b sin θ = c, then a sin θ + b cos θ =
Prove the following identity :
`1/(cosA + sinA - 1) + 2/(cosA + sinA + 1) = cosecA + secA`
If cosθ = `5/13`, then find sinθ.
Prove that: 2(sin6 θ + cos6 θ) – 3 (sin4 θ + cos4 θ) + 1 = 0.
Prove that `( 1 + sin θ)/(1 - sin θ) = 1 + 2 tan θ/cos θ + 2 tan^2 θ` .
Prove that `( tan A + sec A - 1)/(tan A - sec A + 1) = (1 + sin A)/cos A`.
If x sin3θ + y cos3 θ = sin θ cos θ and x sin θ = y cos θ , then show that x2 + y2 = 1.
Prove the following:
(sin α + cos α)(tan α + cot α) = sec α + cosec α
