Advertisements
Advertisements
प्रश्न
Prove the following identities:
sec4 A (1 – sin4 A) – 2 tan2 A = 1
Advertisements
उत्तर
sec4 A (1 – sin4 A) – 2 tan2 A
= sec4 A – sec4 A sin4 A – 2 tan2 A
= `(sec^2A)^2 - 1/(cos^4A)sin^4A - 2tan^2A`
= (1 + tan2 A)2 – tan4 A – 2 tan2 A ...`[(sec^2A - tan^2A = 1), (sec^2A = 1 + tan^2A)]`
= (1)2 + (tan2 A)2 – 2 × 1 × tan2 A – tan4 A – 2 tan2 A
= 1 + tan4 A + 2 tan2 A – tan4 A – 2 tan2 A
= 1
संबंधित प्रश्न
Evaluate
`(sin ^2 63^@ + sin^2 27^@)/(cos^2 17^@+cos^2 73^@)`
Prove the following trigonometric identities.
sec A (1 − sin A) (sec A + tan A) = 1
Prove the following identities:
sec2A + cosec2A = sec2A . cosec2A
If a cos `theta + b sin theta = m and a sin theta - b cos theta = n , "prove that "( m^2 + n^2 ) = ( a^2 + b^2 )`
Write the value of`(tan^2 theta - sec^2 theta)/(cot^2 theta - cosec^2 theta)`
If cos A + cos2 A = 1, then sin2 A + sin4 A =
Prove that : `tan"A"/(1 - cot"A") + cot"A"/(1 - tan"A") = sec"A".cosec"A" + 1`.
If tan θ + cot θ = 2, then tan2θ + cot2θ = ?
If tan θ – sin2θ = cos2θ, then show that sin2 θ = `1/2`.
Given that sin θ = `a/b`, then cos θ is equal to ______.
