Advertisements
Advertisements
Question
What is the value of (1 + cot2 θ) sin2 θ?
Advertisements
Solution
We have,
`(1+cot^2 θ)sin^2θ= cosec^2θxxsin^2θ`
`= (1/sinθ)^2 xx sin^2θ`
= `1/sin^2θxxsin^2θ`
`=1`
APPEARS IN
RELATED QUESTIONS
Prove that:
sec2θ + cosec2θ = sec2θ x cosec2θ
Prove the following trigonometric identities
`cos theta/(1 - sin theta) = (1 + sin theta)/cos theta`
Prove the following trigonometric identities.
`(1 + tan^2 A) + (1 + 1/tan^2 A) = 1/(sin^2 A - sin^4 A)`
Prove the following trigonometric identities.
if `T_n = sin^n theta + cos^n theta`, prove that `(T_3 - T_5)/T_1 = (T_5 - T_7)/T_3`
Prove the following identities:
sec2A + cosec2A = sec2A . cosec2A
Prove that:
`tanA/(1 - cotA) + cotA/(1 - tanA) = secA "cosec" A + 1`
Prove that:
`cot^2A/(cosecA - 1) - 1 = cosecA`
`cos^2 theta + 1/((1+ cot^2 theta )) =1`
Show that none of the following is an identity:
`sin^2 theta + sin theta =2`
Write the value of `sin theta cos ( 90° - theta )+ cos theta sin ( 90° - theta )`.
Write the value of tan10° tan 20° tan 70° tan 80° .
If `sec theta + tan theta = x," find the value of " sec theta`
If sec θ + tan θ = x, write the value of sec θ − tan θ in terms of x.
If cosec θ − cot θ = α, write the value of cosec θ + cot α.
Prove the following identity :
`(1 - sin^2θ)sec^2θ = 1`
Without using trigonometric table , evaluate :
`cosec49°cos41° + (tan31°)/(cot59°)`
Without using trigonometric table , evaluate :
`sin72^circ/cos18^circ - sec32^circ/(cosec58^circ)`
Prove that: `(sec θ - tan θ)/(sec θ + tan θ ) = 1 - 2 sec θ.tan θ + 2 tan^2θ`
Prove the following identities.
sec4 θ (1 – sin4 θ) – 2 tan2 θ = 1
Prove that (sec θ + tan θ) (1 – sin θ) = cos θ
