Advertisements
Advertisements
प्रश्न
Prove the following identities:
`(1 + sin A)/(1 - sin A) = (cosec A + 1)/(cosec A - 1)`
Advertisements
उत्तर
R.H.S = `(1/(sin A) + 1)/(1/(sin A) - 1)`
= `((1 + sin A)/sin A)/((1 - sin A)/sin A)`
= `((1 + sin A))/cancelsin A xx cancelsin A/((1 - sin A))`
= `(1 + sin A)/(1 - sin A)`
∴ R.H.S = L.H.S
संबंधित प्रश्न
As observed from the top of an 80 m tall lighthouse, the angles of depression of two ships on the same side of the lighthouse of the horizontal line with its base are 30° and 40° respectively. Find the distance between the two ships. Give your answer correct to the nearest meter.
Prove the following trigonometric identities.
`(1 + cos θ + sin θ)/(1 + cos θ - sin θ) = (1 + sin θ)/cos θ`
If tan A =` 5/12` , find the value of (sin A+ cos A) sec A.
What is the value of 9cot2 θ − 9cosec2 θ?
If sinA + cosA = `sqrt(2)` , prove that sinAcosA = `1/2`
Prove that `(sec θ - 1)/(sec θ + 1) = ((sin θ)/(1 + cos θ ))^2`
Prove that cot θ. tan (90° - θ) - sec (90° - θ). cosec θ + 1 = 0.
Choose the correct alternative:
`(1 + cot^2"A")/(1 + tan^2"A")` = ?
`5/(sin^2theta) - 5cot^2theta`, complete the activity given below.
Activity:
`5/(sin^2theta) - 5cot^2theta`
= `square (1/(sin^2theta) - cot^2theta)`
= `5(square - cot^2theta) ......[1/(sin^2theta) = square]`
= 5(1)
= `square`
The value of tan A + sin A = M and tan A - sin A = N.
The value of `("M"^2 - "N"^2) /("MN")^0.5`
