Advertisements
Advertisements
प्रश्न
Prove the following identity :
`sin^4A + cos^4A = 1 - 2sin^2Acos^2A`
Advertisements
उत्तर
`sin^4A + cos^4A = 1 - 2sin^2Acos^2A`
⇒ `sin^4A + cos^4A + 2sin^2Acos^2A = 1`
LHS = `(sin^2A + cos^2A)^2`
= 1 = RHS
APPEARS IN
संबंधित प्रश्न
Prove that:
`(cos^3A + sin^3A)/(cosA + sinA) + (cos^3A - sin^3A)/(cosA - sinA) = 2`
`{1/((sec^2 theta- cos^2 theta))+ 1/((cosec^2 theta - sin^2 theta))} ( sin^2 theta cos^2 theta) = (1- sin^2 theta cos ^2 theta)/(2+ sin^2 theta cos^2 theta)`
Prove that `( sintheta - 2 sin ^3 theta ) = ( 2 cos ^3 theta - cos theta) tan theta`
If `cosec theta = 2x and cot theta = 2/x ," find the value of" 2 ( x^2 - 1/ (x^2))`
What is the value of (1 + cot2 θ) sin2 θ?
Prove the following identity :
`sec^4A - sec^2A = sin^2A/cos^4A`
Prove that `(sec θ - 1)/(sec θ + 1) = ((sin θ)/(1 + cos θ ))^2`
If A + B = 90°, show that sec2 A + sec2 B = sec2 A. sec2 B.
Prove that sec2θ – cos2θ = tan2θ + sin2θ
Let α, β be such that π < α – β < 3π. If sin α + sin β = `-21/65` and cos α + cos β = `-27/65`, then the value of `cos (α - β)/2` is ______.
