Advertisements
Advertisements
प्रश्न
Prove that `((1 + sin θ - cos θ)/( 1 + sin θ + cos θ))^2 = (1 - cos θ)/(1 + cos θ)`.
Advertisements
उत्तर
LHS = `((1 + sin θ - cos θ)/( 1 + sin θ + cos θ))^2`
⇒ `(1 + sin^2 θ + cos^2 θ + 2(sin θ - cos θ - sin θ. cos θ))/(1 + sin^2 θ + cos^2 θ + 2(sin θ + cos θ + sin θ. cos θ)`
= `(1 + 1 + 2 (sin θ - cos θ - sin θ. cos θ))/( 1 + 1 + 2((sin θ + cos θ + sin θ. cos θ)`
= `(2 (1 + sin θ - cos θ - sin θ. cos θ))/(2( 1 + (sin θ + cos θ + sin θ. cos θ))`
= `( 1 + sin θ - cos θ( 1 + sin θ))/(1 + sin θ + cos θ( 1 + sin θ))`
= `((1 + sin θ)(1 - cos θ))/((1 + sin θ)( 1 + cos θ))`
= `(1 - cos θ)/( 1 + cos θ)`
= RHS
Hence proved.
संबंधित प्रश्न
Prove that `\frac{\sin \theta -\cos \theta }{\sin \theta +\cos \theta }+\frac{\sin\theta +\cos \theta }{\sin \theta -\cos \theta }=\frac{2}{2\sin^{2}\theta -1}`
Prove the following trigonometric identities.
`cot theta - tan theta = (2 cos^2 theta - 1)/(sin theta cos theta)`
Prove that `sqrt((1 + cos theta)/(1 - cos theta)) + sqrt((1 - cos theta)/(1 + cos theta)) = 2 cosec theta`
Prove the following identities:
`(1+ sin A)/(cosec A - cot A) - (1 - sin A)/(cosec A + cot A) = 2(1 + cot A)`
If ` cot A= 4/3 and (A+ B) = 90° ` ,what is the value of tan B?
What is the value of (1 + cot2 θ) sin2 θ?
\[\frac{\tan \theta}{\sec \theta - 1} + \frac{\tan \theta}{\sec \theta + 1}\] is equal to
If A = 30°, verify that `sin 2A = (2 tan A)/(1 + tan^2 A)`.
If a cos θ – b sin θ = c, then prove that (a sin θ + b cos θ) = `± sqrt(a^2 + b^2 - c^2)`
If 5 sec θ – 12 cosec θ = 0, then find values of sin θ, sec θ.
