Advertisements
Advertisements
Question
\[\frac{\sin \theta}{1 + \cos \theta}\]is equal to
Options
\[\frac{\sin \theta}{1 + \cos \theta}\]
\[\frac{1 - \cos \theta}{\cos \theta}\]
\[\frac{1 - \cos \theta}{\cos \theta}\]
\[\frac{1 - \sin \theta}{\cos \theta}\]
Solution
The given expression is `sin θ/(1+cosθ)`
Multiplying both the numerator and denominator under the root by`(1-cosθ )` , we have
`sinθ/(1+cos θ)`
= `(sinθ (1-cos θ))/((1+cosθ)(1-cos θ))`
=`(sin θ(1-cos θ))/(1-cos^2 θ)`
= `(sin θ(1-cos θ))/sin^2 θ`
= `(1-cos θ)/sin θ`
APPEARS IN
RELATED QUESTIONS
Prove the following trigonometric identities
`cos theta/(1 - sin theta) = (1 + sin theta)/cos theta`
Prove the following trigonometric identities
cosec6θ = cot6θ + 3 cot2θ cosec2θ + 1
Prove the following identities:
(cos A + sin A)2 + (cos A – sin A)2 = 2
Prove the following identities:
`(1 - sinA)/(1 + sinA) = (secA - tanA)^2`
Show that : tan 10° tan 15° tan 75° tan 80° = 1
`((sin A- sin B ))/(( cos A + cos B ))+ (( cos A - cos B ))/(( sinA + sin B ))=0`
Prove that `(sinθ - cosθ + 1)/(sinθ + cosθ - 1) = 1/(secθ - tanθ)`
What is the value of 9cot2 θ − 9cosec2 θ?
sec4 A − sec2 A is equal to
2 (sin6 θ + cos6 θ) − 3 (sin4 θ + cos4 θ) is equal to
Prove the following identity :
( 1 + cotθ - cosecθ) ( 1 + tanθ + secθ)
Prove the following identity :
`sqrt((1 + cosA)/(1 - cosA)) = cosecA + cotA`
Prove the following identity :
`1/(cosA + sinA - 1) + 2/(cosA + sinA + 1) = cosecA + secA`
Find the value of `θ(0^circ < θ < 90^circ)` if :
`tan35^circ cot(90^circ - θ) = 1`
Prove that: `(sec θ - tan θ)/(sec θ + tan θ ) = 1 - 2 sec θ.tan θ + 2 tan^2θ`
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: sec2 θ + cosec2 θ = sec2 θ cosec2 θ.
Prove the following identities.
`(1 - tan^2theta)/(cot^2 theta - 1)` = tan2 θ
If (sin α + cosec α)2 + (cos α + sec α)2 = k + tan2α + cot2α, then the value of k is equal to
`(cos^2 θ)/(sin^2 θ) - 1/(sin^2 θ)`, in simplified form, is ______.
