Advertisements
Advertisements
प्रश्न
Prove the following identity :
`((1 + tan^2A)cotA)/(cosec^2A) = tanA`
Advertisements
उत्तर
`((1 + tan^2A)cotA)/(cosec^2A)`
= `(sec^2AcotA)/(cosec^2A) ......(∴ sec^2A = 1 + tan^2A)`
= `(1/cos^2A . cosA/sinA)/(1/sin^2A) = 1/((cosAsinA)/(1/sin^2A)`
= `sinA/cosA = tanA`
APPEARS IN
संबंधित प्रश्न
Evaluate without using trigonometric tables:
`cos^2 26^@ + cos 64^@ sin 26^@ + (tan 36^@)/(cot 54^@)`
If 3 sin θ + 5 cos θ = 5, prove that 5 sin θ – 3 cos θ = ± 3.
Prove the following identities:
cosec A(1 + cos A) (cosec A – cot A) = 1
Prove the following identities:
(cosec A + sin A) (cosec A – sin A) = cot2 A + cos2 A
If tan A = n tan B and sin A = m sin B, prove that `cos^2A = (m^2 - 1)/(n^2 - 1)`
`cosec theta (1+costheta)(cosectheta - cot theta )=1`
If x=a `cos^3 theta and y = b sin ^3 theta ," prove that " (x/a)^(2/3) + ( y/b)^(2/3) = 1.`
Prove the following identity:
tan2A − sin2A = tan2A · sin2A
sec 60° = ?
Prove that `(1 + sin B)/(cos B) + (cos B)/(1 + sin B) = 2 sec B`.
