Advertisements
Advertisements
प्रश्न
Prove that:
`(tanA + 1/cosA)^2 + (tanA - 1/cosA)^2 = 2((1 + sin^2A)/(1 - sin^2A))`
Advertisements
उत्तर
L.H.S. = `(tanA + 1/cosA)^2 + (tanA - 1/cosA)^2`
= `(sinA/cosA + 1/cosA)^2 + (sinA/cosA - 1/cosA)^2`
= `((sinA + 1)/cosA)^2 + ((sinA - 1)/cosA)^2`
= `(sinA + 1)^2/(cos^2A) + (sinA - 1)^2/(cos^2A)`
= `((sinA + 1)^2 + (sinA - 1)^2)/(cos^2A)`
= `(sin^2A + 1 + 2sinA + sin^2A + 1 - 2sinA)/cos^2A`
= `(2sin^2A + 2)/(cos^2A)`
= `(2(1 + sin^2A))/(1 - sin^2A)`
= `2((1 + sin^2A)/(1 - sin^2A))` = R.H.S.
APPEARS IN
संबंधित प्रश्न
If x = a cos θ and y = b cot θ, show that:
`a^2/x^2 - b^2/y^2 = 1`
`(sin theta)/((sec theta + tan theta -1)) + cos theta/((cosec theta + cot theta -1))=1`
Write the value of `( 1- sin ^2 theta ) sec^2 theta.`
Write True' or False' and justify your answer the following:
\[ \cos \theta = \frac{a^2 + b^2}{2ab}\]where a and b are two distinct numbers such that ab > 0.
Prove that: 2(sin6 θ + cos6 θ) – 3 (sin4 θ + cos4 θ) + 1 = 0.
`(sin A)/(1 + cos A) + (1 + cos A)/(sin A)` = 2 cosec A
Prove that `((1 - cos^2 θ)/cos θ)((1 - sin^2θ)/(sin θ)) = 1/(tan θ + cot θ)`
Prove the following identities.
cot θ + tan θ = sec θ cosec θ
If tan θ = 3, then `(4 sin theta - cos theta)/(4 sin theta + cos theta)` is equal to ______.
Prove that `sqrt(sec^2 theta + "cosec"^2 theta) = tan theta + cot theta`
