Advertisements
Advertisements
प्रश्न
Prove that:
(sec A − tan A)2 (1 + sin A) = (1 − sin A)
Advertisements
उत्तर
L.H.S. = (sec A − tan A)2 (1 + sin A)
`(1/cos "A" - sin "A"/cos "A")^2 (1 + sin "A")`
= `((1 - sin "A")/cos "A")^2 (1 + sin "A")`
= `((1 - sin "A")(1 - sin "A")(1 + sin "A"))/cos^2"A"`
= `((1 - sin "A")(1 - sin^2 "A"))/cos^2"A"`
= `((1 - sin "A")cos^2"A")/cos^2"A"`
= (1 − sin A) R.H.S.
संबंधित प्रश्न
Prove that:
sec2θ + cosec2θ = sec2θ x cosec2θ
Prove the following trigonometric identities.
`tan θ/(1 - cot θ) + cot θ/(1 - tan θ) = 1 + tan θ + cot θ`
If 3 sin θ + 5 cos θ = 5, prove that 5 sin θ – 3 cos θ = ± 3.
Prove that:
`tanA/(1 - cotA) + cotA/(1 - tanA) = secA "cosec" A + 1`
Prove the following identity:
tan2A − sin2A = tan2A · sin2A
Express (sin 67° + cos 75°) in terms of trigonometric ratios of the angle between 0° and 45°.
A moving boat is observed from the top of a 150 m high cliff moving away from the cliff. The angle of depression of the boat changes from 60° to 45° in 2 minutes. Find the speed of the boat in m/min.
Prove that : `1 - (cos^2 θ)/(1 + sin θ) = sin θ`.
Prove that `(sin (90° - θ))/cos θ + (tan (90° - θ))/cot θ + (cosec (90° - θ))/sec θ = 3`.
Prove that:
`(sin A + cos A)/(sin A - cos A) + (sin A - cos A)/(sin A + cos A) = 2/(2 sin^2 A - 1)`
