Advertisements
Advertisements
प्रश्न
Prove that:
`sqrt(sec^2A + cosec^2A) = tanA + cotA`
Advertisements
उत्तर
L.H.S. = `sqrt(sec^2A + cosec^2A)`
= `sqrt(1/cos^2A + 1/sin^2A)`
= `sqrt((sin^2A + cos^2A)/(sin^2Acos^2A)`
= `sqrt(1/(sin^2Acos^2A)`
= `sqrt(1/(sinAcosA))`
R.H.S. = tan A + cot A
= `sinA/cosA + cosA/sinA`
= `(sin^2A + cos^2A)/(sinAcosA)`
= `1/(sinAcosA)`
L.H.S. = R.H.S.
APPEARS IN
संबंधित प्रश्न
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`cos A/(1 + sin A) + (1 + sin A)/cos A = 2 sec A`
Prove that:
`(cos^3A + sin^3A)/(cosA + sinA) + (cos^3A - sin^3A)/(cosA - sinA) = 2`
`sqrt((1 + sin θ)/(1 - sin θ)) = sec θ + tan θ`
`((sin A- sin B ))/(( cos A + cos B ))+ (( cos A - cos B ))/(( sinA + sin B ))=0`
Write the value of ` cosec^2 (90°- theta ) - tan^2 theta`
If \[\sin \theta = \frac{1}{3}\] then find the value of 2cot2 θ + 2.
Prove the following identity :
`(1 + sinθ)/(cosecθ - cotθ) - (1 - sinθ)/(cosecθ + cotθ) = 2(1 + cotθ)`
Evaluate:
`(tan 65^circ)/(cot 25^circ)`
`sin θ = 1/2`, then θ = ?
Prove that sin θ (1 – tan θ) – cos θ (1 – cot θ) = cosec θ – sec θ.
