Advertisements
Advertisements
प्रश्न
Prove the following identities:
(cosec A + sin A) (cosec A – sin A) = cot2 A + cos2 A
Advertisements
उत्तर
L.H.S. = (cosec A + sin A) (cosec A – sin A)
= (cosec2 A – sin2 A) ...[∵ (a + b) (a – b) = a2 – b2]
= 1 + cot2 A – sin2 A
= cot2 A + 1 – sin2 A
= cot2 A + cos2 A ...(∵ 1 – sin2 A = cos2 A)
= R.H.S.
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`sqrt((1 - cos theta)/(1 + cos theta)) = cosec theta - cot theta`
What is the value of (1 − cos2 θ) cosec2 θ?
What is the value of (1 + tan2 θ) (1 − sin θ) (1 + sin θ)?
Write True' or False' and justify your answer the following :
The value of \[\sin \theta\] is \[x + \frac{1}{x}\] where 'x' is a positive real number .
Prove the following identity :
`(cotA + tanB)/(cotB + tanA) = cotAtanB`
Prove the following identity :
`sqrt(cosec^2q - 1) = "cosq cosecq"`
Prove the following identity :
`tan^2θ/(tan^2θ - 1) + (cosec^2θ)/(sec^2θ - cosec^2θ) = 1/(sin^2θ - cos^2θ)`
Prove that ( 1 + tan A)2 + (1 - tan A)2 = 2 sec2A
If x sin3θ + y cos3 θ = sin θ cos θ and x sin θ = y cos θ , then show that x2 + y2 = 1.
Prove that sec2θ – cos2θ = tan2θ + sin2θ.
