Advertisements
Advertisements
Question
The value of \[\sqrt{\frac{1 + \cos \theta}{1 - \cos \theta}}\]
Options
cot θ − cosec θ
cosec θ + cot θ
cosec2 θ + cot2 θ
(cot θ + cosec θ)2
Solution
The given expression is `sqrt ((1+cosθ)/(1-cos θ))`
Multiplying both the numerator and denominator under the root by` (1+cosθ )`, we have
`sqrt (((1+cosθ)(1+cosθ))/((1+cosθ)(1-cos θ)))`
`=sqrt ((1+cosθ)^2/ ((1-cos^2 θ))`
`=sqrt((1+cos θ)^2/sin^2θ`
`=(1+cos θ)/(sinθ)`
= `1/sinθ+cosθ/sinθ`
= `cosecθ+cotθ`
APPEARS IN
RELATED QUESTIONS
Prove the following identities:
cosec A(1 + cos A) (cosec A – cot A) = 1
Prove the following identities:
`(1 + sinA)/cosA + cosA/(1 + sinA) = 2secA`
Prove the following identities:
`sqrt((1 - cosA)/(1 + cosA)) = sinA/(1 + cosA)`
Prove that:
(tan A + cot A) (cosec A – sin A) (sec A – cos A) = 1
`(tan^2theta)/((1+ tan^2 theta))+ cot^2 theta/((1+ cot^2 theta))=1`
` (sin theta + cos theta )/(sin theta - cos theta ) + ( sin theta - cos theta )/( sin theta + cos theta) = 2/ ((1- 2 cos^2 theta))`
Show that none of the following is an identity:
(i) `cos^2theta + cos theta =1`
Show that none of the following is an identity:
`tan^2 theta + sin theta = cos^2 theta`
Write the value of `sin theta cos ( 90° - theta )+ cos theta sin ( 90° - theta )`.
Prove the following identity :
`(1 + cotA)^2 + (1 - cotA)^2 = 2cosec^2A`
Find the value of `θ(0^circ < θ < 90^circ)` if :
`tan35^circ cot(90^circ - θ) = 1`
Prove that:
`sqrt((sectheta - 1)/(sec theta + 1)) + sqrt((sectheta + 1)/(sectheta - 1)) = 2cosectheta`
Prove that sin4θ - cos4θ = sin2θ - cos2θ
= 2sin2θ - 1
= 1 - 2 cos2θ
Prove that `sqrt((1 - sin θ)/(1 + sin θ)) = sec θ - tan θ`.
Prove that : `1 - (cos^2 θ)/(1 + sin θ) = sin θ`.
Prove that
sec2A – cosec2A = `(2sin^2"A" - 1)/(sin^2"A"*cos^2"A")`
If `sqrt(3) tan θ` = 1, then find the value of sin2θ – cos2θ.
If sin θ + cos θ = p and sec θ + cosec θ = q, then prove that q(p2 – 1) = 2p.
If sinθ = `11/61`, then find the value of cosθ using the trigonometric identity.
Prove the following that:
`tan^3θ/(1 + tan^2θ) + cot^3θ/(1 + cot^2θ)` = secθ cosecθ – 2 sinθ cosθ
