Advertisements
Advertisements
प्रश्न
Prove the following identities:
`cosecA + cotA = 1/(cosecA - cotA)`
Advertisements
उत्तर
L.H.S. = `cosecA + cotA`
= `(cosecA + cotA)/1 xx (cosecA - cotA)/(cosecA - cotA)`
= `(cosec^2A - cot^2A)/(cosecA - cotA)`
= `(1 + cot^2A - cot^2A)/(cosecA - cotA)`
= `1/(cosecA - cotA)` = R.H.S.
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
(1 + tan2θ) (1 − sinθ) (1 + sinθ) = 1
Prove the following identities:
cosec A(1 + cos A) (cosec A – cot A) = 1
`1 + (tan^2 θ)/((1 + sec θ)) = sec θ`
Prove the following identities:
`(cot^2 theta (sec theta - 1))/((1 + sin theta)) + (sec^2 theta(sin theta - 1))/((1 + sec theta)) = 0`
Write the value of `4 tan^2 theta - 4/ cos^2 theta`
If tan A =` 5/12` , find the value of (sin A+ cos A) sec A.
Write True' or False' and justify your answer the following:
\[ \cos \theta = \frac{a^2 + b^2}{2ab}\]where a and b are two distinct numbers such that ab > 0.
If x = a sec θ + b tan θ and y = a tan θ + b sec θ prove that x2 - y2 = a2 - b2.
Prove the following identities:
`1/(sin θ + cos θ) + 1/(sin θ - cos θ) = (2sin θ)/(1 - 2 cos^2 θ)`.
sec2θ – tan2θ = ?
