Advertisements
Advertisements
Question
Which of the following is true for all values of θ (0° ≤ θ ≤ 90°)?
Options
cos2 θ – sin2 θ = 1
cosec2 θ – sec2 θ = 1
sec2 θ – tan2 θ = 1
cot2 θ – tan2 θ = 1
Advertisements
Solution
sec2 θ – tan2 θ = 1
Explanation:
∵ sec2 θ = 1 + tan2 θ
∴ sec2 θ – tan2 θ = 1
APPEARS IN
RELATED QUESTIONS
Prove the following trigonometric identities:
sin2 A cot2 A + cos2 A tan2 A = 1
Prove the following trigonometric identities.
`(cot A - cos A)/(cot A + cos A) = (cosec A - 1)/(cosec A + 1)`
Prove the following identities:
cot2 A – cos2 A = cos2 A . cot2 A
If `(x/a sin theta - y/b cos theta) = 1` and `(x/a cos theta + y/b sin theta) = 1`, prove that `(x^2/a^2 + y^2/b^2) = 2`.
If \[\sin \theta = \frac{1}{3}\] then find the value of 2cot2 θ + 2.
Prove the following identity :
`sec^2A + cosec^2A = sec^2Acosec^2A`
Prove the following identity :
`((1 + tan^2A)cotA)/(cosec^2A) = tanA`
Prove that cosec2 (90° - θ) + cot2 (90° - θ) = 1 + 2 tan2 θ.
Prove that : `tan"A"/(1 - cot"A") + cot"A"/(1 - tan"A") = sec"A".cosec"A" + 1`.
Prove the following identities.
sec4 θ (1 – sin4 θ) – 2 tan2 θ = 1
