Advertisements
Advertisements
प्रश्न
Prove that:
(1 + tan A . tan B)2 + (tan A – tan B)2 = sec2 A sec2 B
Advertisements
उत्तर
L.H.S. = (1 + tanA . tan B)2 + (tan A – tan B)2
= 1 + tan2A . tan2B + 2 tan A . tan B + tan2A + tan2B – 2 tan A tan B
= 1 + tan2A + tan2B + tan2A + tan2B
= sec2A + tan2 B(1 + tan2A)
= sec2A + tan2 B sec2 A
= sec2A(1 + tan2B)
= sec2A sec2B
= R.H.S.
संबंधित प्रश्न
Prove that
`sqrt((1 + sin θ)/(1 - sin θ)) + sqrt((1 - sin θ)/(1 + sin θ)) = 2 sec θ`
`(cot^2 theta ( sec theta - 1))/((1+ sin theta))+ (sec^2 theta(sin theta-1))/((1+ sec theta))=0`
If `cot theta = 1/ sqrt(3) , "write the value of" ((1- cos^2 theta))/((2 -sin^2 theta))`
Prove the following identity :
`(cosecθ)/(tanθ + cotθ) = cosθ`
If sec θ = `25/7`, then find the value of tan θ.
Prove that `(tan^2"A")/(tan^2 "A"-1) + (cosec^2"A")/(sec^2"A"-cosec^2"A") = (1)/(1-2 co^2 "A")`
Prove the following identities.
`(sin "A" - sin "B")/(cos "A" + cos "B") + (cos "A" - cos "B")/(sin "A" + sin "B")`
Prove the following identities.
`(sin^3"A" + cos^3"A")/(sin"A" + cos"A") + (sin^3"A" - cos^3"A")/(sin"A" - cos"A")` = 2
If sin θ + cos θ = a and sec θ + cosec θ = b , then the value of b(a2 – 1) is equal to
Prove that `(sintheta + "cosec" theta)/sin theta` = 2 + cot2θ
