Advertisements
Advertisements
प्रश्न
If sin θ + cos θ = a and sec θ + cosec θ = b , then the value of b(a2 – 1) is equal to
विकल्प
2a
3a
0
2ab
उत्तर
2a
Explanation;
Hint:
b(a2 – 1) = (sec θ + cosec θ) [(sin θ + cos θ)2 – 1]
= `1/ cos theta + 1/sin theta` [sin2 θ + cos2 θ + 2 sin θ cos θ – 1]
= `[(sin theta + cos theta)/(sin theta cos theta)]` [1 + 2 sin θ cos θ – 1]
= `[(sin theta + cos theta)/(sin theta cos theta)] xx 2 sin theta cos theta`
= 2(sin θ + cos θ)
= 2a
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
if cos A + cos2 A = 1, prove that sin2 A + sin4 A = 1
`tan theta /((1 - cot theta )) + cot theta /((1 - tan theta)) = (1+ sec theta cosec theta)`
`sin^2 theta + cos^4 theta = cos^2 theta + sin^4 theta`
If a cos `theta + b sin theta = m and a sin theta - b cos theta = n , "prove that "( m^2 + n^2 ) = ( a^2 + b^2 )`
Prove the following identity :
`tanA - cotA = (1 - 2cos^2A)/(sinAcosA)`
Find the value of `θ(0^circ < θ < 90^circ)` if :
`cos 63^circ sec(90^circ - θ) = 1`
Prove that sec2θ − cos2θ = tan2θ + sin2θ
Prove that `costheta/(1 + sintheta) = (1 - sintheta)/(costheta)`
Prove that `sec"A"/(tan "A" + cot "A")` = sin A
Prove that cosec θ – cot θ = `sin theta/(1 + cos theta)`
