Advertisements
Advertisements
प्रश्न
Prove that `sqrt((1 + sin θ)/(1 - sin θ))` = sec θ + tan θ.
Advertisements
उत्तर
LHS = `sqrt((1 + sin θ)/(1 - sin θ) xx (1 + sin θ)/(1 + sin θ))`
= `sqrt((1 + sin θ)^2/(1 - sin^2θ))`
= `sqrt((1 + sin θ)^2/(cos^2θ)`
= `(1 + sin θ)/cos θ = 1/cos θ + sin θ/cos θ`
= sec θ + tan θ
= RHS
Hence proved.
संबंधित प्रश्न
Prove the following trigonometric identities:
`(\text{i})\text{ }\frac{\sin \theta }{1-\cos \theta }=\text{cosec}\theta+\cot \theta `
Evaluate sin25° cos65° + cos25° sin65°
`(1+tan^2A)/(1+cot^2A)` = ______.
Prove the following trigonometric identities.
if `T_n = sin^n theta + cos^n theta`, prove that `(T_3 - T_5)/T_1 = (T_5 - T_7)/T_3`
Prove that:
(1 + tan A . tan B)2 + (tan A – tan B)2 = sec2 A sec2 B
`1+ (cot^2 theta)/((1+ cosec theta))= cosec theta`
`sqrt((1-cos theta)/(1+cos theta)) = (cosec theta - cot theta)`
If sec2 θ (1 + sin θ) (1 − sin θ) = k, then find the value of k.
If cosec θ = 2x and \[5\left( x^2 - \frac{1}{x^2} \right)\] \[2\left( x^2 - \frac{1}{x^2} \right)\]
Prove the following identity :
`(1 + tan^2A) + (1 + 1/tan^2A) = 1/(sin^2A - sin^4A)`
