Advertisements
Advertisements
Question
Prove the following identities:
`(costhetacottheta)/(1 + sintheta) = cosectheta - 1`
Advertisements
Solution
L.H.S. = `(costhetacottheta)/(1 + sintheta)`
= `(costhetacottheta)/(1 + sintheta) xx (1 - sintheta)/(1 - sintheta)`
= `(costhetacottheta(1 - sintheta))/(1 - sin^2theta)`
= `(costheta costheta/sintheta(1 - sintheta))/cos^2theta`
= `(1 - sintheta)/sintheta`
= `1/sintheta - 1`
= cosec θ – 1
APPEARS IN
RELATED QUESTIONS
Without using trigonometric tables evaluate
`(sin 35^@ cos 55^@ + cos 35^@ sin 55^@)/(cosec^2 10^@ - tan^2 80^@)`
Prove the following trigonometric identities.
`1 + cot^2 theta/(1 + cosec theta) = cosec theta`
If sin A + cos A = p and sec A + cosec A = q, then prove that : q(p2 – 1) = 2p.
`cos^2 theta + 1/((1+ cot^2 theta )) =1`
Show that none of the following is an identity:
`sin^2 theta + sin theta =2`
Prove that `sqrt((1 + cos A)/(1 - cos A)) = (tan A + sin A)/(tan A. sin A)`
Prove that: `cos^2 A + 1/(1 + cot^2 A) = 1`.
If x sin3 θ + y cos3 θ = sin θ cos θ and x sin θ = y cos θ, then prove that x2 + y2 = 1
Prove that sin θ (1 – tan θ) – cos θ (1 – cot θ) = cosec θ – sec θ.
Statement 1: sin2θ + cos2θ = 1
Statement 2: cosec2θ + cot2θ = 1
Which of the following is valid?
