Advertisements
Advertisements
प्रश्न
Prove the following identity :
`sec^2A.cosec^2A = tan^2A + cot^2A + 2`
Advertisements
उत्तर
LHS = `sec^2A.cosec^2A = 1/(cos^2A.sin^2A)`
RHS = `tan^2A + cot^2A + 2 = tan^2A + cot^2A + 2tan^2A.cot^2A`
= `(tanA + cotA)^2 = (sinA/cosA + cosA/sinA)^2`
= `((sin^2A + cos^2A)/(sinA.cosA))^2 = 1/(cos^2A.sin^2A)`
= Hence , LHS = RHS
APPEARS IN
संबंधित प्रश्न
Evaluate without using trigonometric tables:
`cos^2 26^@ + cos 64^@ sin 26^@ + (tan 36^@)/(cot 54^@)`
Prove the following identities:
`sinA/(1 + cosA) = cosec A - cot A`
Write the value of `cosec^2 theta (1+ cos theta ) (1- cos theta).`
Write the value of `3 cot^2 theta - 3 cosec^2 theta.`
What is the value of (1 − cos2 θ) cosec2 θ?
Prove the following identity :
`(cosecA - sinA)(secA - cosA)(tanA + cotA) = 1`
Find the value of sin 30° + cos 60°.
If sec θ = `25/7`, then find the value of tan θ.
If 5x = sec θ and `5/x` = tan θ, then `x^2 - 1/x^2` is equal to
Prove the following:
`tanA/(1 + sec A) - tanA/(1 - sec A)` = 2cosec A
