Advertisements
Advertisements
Question
If `sin theta = 1/2 , " write the value of" ( 3 cot^2 theta + 3).`
Solution
As , `sin theta = 1/2 `
So , `cosec theta = 1/ sin theta = 2 ........(i)`
Now ,
`3 cot ^2 theta + 3 `
= `3 ( cot^2 theta + 1)`
=`3 cosec^2 theta`
=` 3(2)^2 [ Using (i)]`
=3(4)
=12
APPEARS IN
RELATED QUESTIONS
Prove the following trigonometric identities:
(i) (1 – sin2θ) sec2θ = 1
(ii) cos2θ (1 + tan2θ) = 1
Prove the identity (sin θ + cos θ)(tan θ + cot θ) = sec θ + cosec θ.
Prove the following trigonometric identities.
`(cot A - cos A)/(cot A + cos A) = (cosec A - 1)/(cosec A + 1)`
Prove the following trigonometric identities.
(sec A + tan A − 1) (sec A − tan A + 1) = 2 tan A
Prove the following identities:
(cosec A – sin A) (sec A – cos A) (tan A + cot A) = 1
Prove that:
2 sin2 A + cos4 A = 1 + sin4 A
Show that : `sinA/sin(90^circ - A) + cosA/cos(90^circ - A) = sec A cosec A`
`(1+ cos theta + sin theta)/( 1+ cos theta - sin theta )= (1+ sin theta )/(cos theta)`
`(sin theta+1-cos theta)/(cos theta-1+sin theta) = (1+ sin theta)/(cos theta)`
Write the value of `( 1- sin ^2 theta ) sec^2 theta.`
Prove that:
`(sin^2θ)/(cosθ) + cosθ = secθ`
What is the value of (1 − cos2 θ) cosec2 θ?
If cos A + cos2 A = 1, then sin2 A + sin4 A =
Prove the following identity :
`(1 - sin^2θ)sec^2θ = 1`
Prove the following identity :
`sinθ(1 + tanθ) + cosθ(1 +cotθ) = secθ + cosecθ`
If cosθ = `5/13`, then find sinθ.
If tan α = n tan β, sin α = m sin β, prove that cos2 α = `(m^2 - 1)/(n^2 - 1)`.
Prove the following identities.
`costheta/(1 + sintheta)` = sec θ – tan θ
Prove that `(1 + sec "A")/"sec A" = (sin^2"A")/(1 - cos"A")`
Prove the following identity:
(sin2θ – 1)(tan2θ + 1) + 1 = 0
