Advertisements
Advertisements
प्रश्न
Prove that (1 – cos2A) . sec2B + tan2B(1 – sin2A) = sin2A + tan2B
उत्तर
L.H.S = (1 – cos2A) . sec2B + tan2B(1 – sin2A)
= `sin^2"A"* 1/(cos^2"B") + (sin^2"B")/(cos^2"B") (1 - sin^2"A")` ......`[(because sin^2"A" + cos^2"A" = 1),(therefore 1 - cos^2"A" = sin^2"A")]`
= `(sin^2"A")/(cos^2"B") + (sin^2"B")/(cos^2"B") - (sin^2"A"sin^2"B")/(cos^2"B")`
= `(sin^2"A")/(cos^2"B") - (sin^2"A"sin^2"B")/(cos^2"B") + (sin^2"B")/(cos^2"B")`
= `(sin^2"A")/(cos^2"B") (1 - sin^2"B") + tan^2"B"`
= `(sin^2"A")/(cos^2"B") (cos^2"B") + tan^2"B"`
= sin2A + tan2B
= R.H.S
∴ (1 – cos2A) . sec2B + tan2B (1 – sin2A) = sin2A + tan2B
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities
(1 + cot2 A) sin2 A = 1
Prove the following identities:
cosec A(1 + cos A) (cosec A – cot A) = 1
Prove that:
`cosA/(1 + sinA) = secA - tanA`
`(1+tan^2theta)(1+cot^2 theta)=1/((sin^2 theta- sin^4theta))`
If`( 2 sin theta + 3 cos theta) =2 , " prove that " (3 sin theta - 2 cos theta) = +- 3.`
Write the value of tan10° tan 20° tan 70° tan 80° .
If a cos θ + b sin θ = m and a sin θ − b cos θ = n, then a2 + b2 =
Prove the following identity :
`(1 - cos^2θ)sec^2θ = tan^2θ`
Prove the following identity :
secA(1 + sinA)(secA - tanA) = 1
Choose the correct alternative:
1 + tan2 θ = ?
Prove that cosec2 (90° - θ) + cot2 (90° - θ) = 1 + 2 tan2 θ.
Prove that `(tan θ)/(cot(90° - θ)) + (sec (90° - θ) sin (90° - θ))/(cosθ. cosec θ) = 2`.
Prove that sin (90° - θ) cos (90° - θ) = tan θ. cos2θ.
Prove that `(sin (90° - θ))/cos θ + (tan (90° - θ))/cot θ + (cosec (90° - θ))/sec θ = 3`.
Prove the following identities.
`(sin "A" - sin "B")/(cos "A" + cos "B") + (cos "A" - cos "B")/(sin "A" + sin "B")`
Choose the correct alternative:
sin θ = `1/2`, then θ = ?
Prove that `(tan(90 - theta) + cot(90 - theta))/("cosec" theta)` = sec θ
If 1 + sin2α = 3 sinα cosα, then values of cot α are ______.
Prove the following that:
`tan^3θ/(1 + tan^2θ) + cot^3θ/(1 + cot^2θ)` = secθ cosecθ – 2 sinθ cosθ
Statement 1: sin2θ + cos2θ = 1
Statement 2: cosec2θ + cot2θ = 1
Which of the following is valid?
