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 the following trigonometric identities.
(sec A − cosec A) (1 + tan A + cot A) = tan A sec A − cot A cosec A
\[\frac{\sin \theta}{1 + \cos \theta}\]is equal to
Prove the following identity :
sinθcotθ + sinθcosecθ = 1 + cosθ
Prove that:
`sqrt(( secθ - 1)/(secθ + 1)) + sqrt((secθ + 1)/(secθ - 1)) = 2 "cosec"θ`
Prove that `(sin (90° - θ))/cos θ + (tan (90° - θ))/cot θ + (cosec (90° - θ))/sec θ = 3`.
Prove the following identities.
cot θ + tan θ = sec θ cosec θ
Prove that `[(1 + sin theta - cos theta)/(1 + sin theta + cos theta)]^2 = (1 - cos theta)/(1 + cos theta)`
Choose the correct alternative:
cos θ. sec θ = ?
Prove the following:
(sin α + cos α)(tan α + cot α) = sec α + cosec α
Show that `(cos^2(45^circ + θ) + cos^2(45^circ - θ))/(tan(60^circ + θ) tan(30^circ - θ)) = 1`
