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प्रश्न
Prove that: sin4 θ + cos4θ = 1 - 2sin2θ cos2 θ.
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उत्तर
LHS = (sin2θ)2 + (cos2 θ)2 + 2 sin2θ cos2θ - 2 sin2θ cos2θ
= ( sin2θ + cos2θ )2 - 2 sin2θ cos2θ
= 1 - 2 sin2θ cos2θ
= RHS
Hence proved.
संबंधित प्रश्न
If `x/a=y/b = z/c` show that `x^3/a^3 + y^3/b^3 + z^3/c^3 = (3xyz)/(abc)`.
Prove that `(sin theta)/(1-cottheta) + (cos theta)/(1 - tan theta) = cos theta + sin theta`
If x = a cos θ and y = b cot θ, show that:
`a^2/x^2 - b^2/y^2 = 1`
If x = a sin θ and y = b cos θ, what is the value of b2x2 + a2y2?
Prove that `sqrt((1 - sin θ)/(1 + sin θ)) = sec θ - tan θ`.
Prove the following identities.
`(sin "A" - sin "B")/(cos "A" + cos "B") + (cos "A" - cos "B")/(sin "A" + sin "B")`
Prove the following identities.
`(sin^3"A" + cos^3"A")/(sin"A" + cos"A") + (sin^3"A" - cos^3"A")/(sin"A" - cos"A")` = 2
If sec θ + tan θ = `sqrt(3)`, complete the activity to find the value of sec θ – tan θ
Activity:
`square` = 1 + tan2θ ......[Fundamental trigonometric identity]
`square` – tan2θ = 1
(sec θ + tan θ) . (sec θ – tan θ) = `square`
`sqrt(3)*(sectheta - tan theta)` = 1
(sec θ – tan θ) = `square`
Prove that `sec"A"/(tan "A" + cot "A")` = sin A
Prove that `sqrt((1 + cos "A")/(1 - cos"A"))` = cosec A + cot A
