Advertisements
Advertisements
Question
Prove the following identity :
`1/(tanA + cotA) = sinAcosA`
Advertisements
Solution
`1/(tanA + cotA) = sinAcosA`
`1/(tanA + cotA)`
= `1/(sinA/cosA + cosA/sinA) = 1/((sin^2A + cos^2A)/(sinAcosA))`
= `1/(1/(sinAcosA)` (`Q sin^2A + cos^2A = 1`)
= sinA cosA
APPEARS IN
RELATED QUESTIONS
Prove the following trigonometric identities.
`1/(1 + sin A) + 1/(1 - sin A) = 2sec^2 A`
Prove the following identities:
`cosecA + cotA = 1/(cosecA - cotA)`
If sin A + cos A = m and sec A + cosec A = n, show that : n (m2 – 1) = 2 m
`sqrt((1-cos theta)/(1+cos theta)) = (cosec theta - cot theta)`
Write the value of ` cosec^2 (90°- theta ) - tan^2 theta`
If \[sec\theta + tan\theta = x\] then \[tan\theta =\]
\[\frac{x^2 - 1}{2x}\] is equal to
Prove the following identity :
`sin^4A + cos^4A = 1 - 2sin^2Acos^2A`
Without using the trigonometric table, prove that
cos 1°cos 2°cos 3° ....cos 180° = 0.
If tan θ – sin2θ = cos2θ, then show that `sin^2θ = 1/2`.
