Advertisements
Advertisements
Question
Prove the following identities:
sec2A + cosec2A = sec2A . cosec2A
Advertisements
Solution
L.H.S. = sec2A + cosec2A
= `1/(cos^2A) + 1/(sin^2A)`
= `(sin^2A + cos^2A)/(cos^2A sin^2A)`
= `1/(cos^2A sin^2A)`
= sec2A cosec2A
= R.H.S. ...(∵ sin2A + cos2A = 1)
RELATED QUESTIONS
Evaluate
`(sin ^2 63^@ + sin^2 27^@)/(cos^2 17^@+cos^2 73^@)`
Prove the following trigonometric identities.
(sec2 θ − 1) (cosec2 θ − 1) = 1
Prove the following identities:
cosec4 A (1 – cos4 A) – 2 cot2 A = 1
Write the value of `3 cot^2 theta - 3 cosec^2 theta.`
If 5 `tan theta = 4,"write the value of" ((cos theta - sintheta))/(( cos theta + sin theta))`
If `cosec theta = 2x and cot theta = 2/x ," find the value of" 2 ( x^2 - 1/ (x^2))`
Prove the following identity :
`cosec^4A - cosec^2A = cot^4A + cot^2A`
Prove the following identity :
`cosecA + cotA = 1/(cosecA - cotA)`
Prove the following identity :
`[1/((sec^2θ - cos^2θ)) + 1/((cosec^2θ - sin^2θ))](sin^2θcos^2θ) = (1 - sin^2θcos^2θ)/(2 + sin^2θcos^2θ)`
Prove that `((1 - cos^2 θ)/cos θ)((1 - sin^2θ)/(sin θ)) = 1/(tan θ + cot θ)`
