Advertisements
Advertisements
Question
Prove the following identity :
`sin^4A + cos^4A = 1 - 2sin^2Acos^2A`
Advertisements
Solution
`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
RELATED QUESTIONS
Prove the following identities:
`( i)sin^{2}A/cos^{2}A+\cos^{2}A/sin^{2}A=\frac{1}{sin^{2}Acos^{2}A)-2`
`(ii)\frac{cosA}{1tanA}+\sin^{2}A/(sinAcosA)=\sin A\text{}+\cos A`
`( iii)((1+sin\theta )^{2}+(1sin\theta)^{2})/cos^{2}\theta =2( \frac{1+sin^{2}\theta}{1-sin^{2}\theta } )`
Prove the following trigonometric identities.
`((1 + tan^2 theta)cot theta)/(cosec^2 theta) = tan theta`
Prove the following identities:
(cos A + sin A)2 + (cos A – sin A)2 = 2
Four alternative answers for the following question are given. Choose the correct alternative and write its alphabet:
sin θ × cosec θ = ______
Prove the following identity :
`sin^2Acos^2B - cos^2Asin^2B = sin^2A - sin^2B`
If `x/(a cosθ) = y/(b sinθ) "and" (ax)/cosθ - (by)/sinθ = a^2 - b^2 , "prove that" x^2/a^2 + y^2/b^2 = 1`
Prove that: `1/(cosec"A" - cot"A") - 1/sin"A" = 1/sin"A" - 1/(cosec"A" + cot"A")`
If sin θ + sin2 θ = 1 show that: cos2 θ + cos4 θ = 1
If tan θ = `9/40`, complete the activity to find the value of sec θ.
Activity:
sec2θ = 1 + `square` ......[Fundamental trigonometric identity]
sec2θ = 1 + `square^2`
sec2θ = 1 + `square`
sec θ = `square`
(tan θ + 2)(2 tan θ + 1) = 5 tan θ + sec2θ.
