Advertisements
Advertisements
प्रश्न
Prove that :(sinθ+cosecθ)2+(cosθ+ secθ)2 = 7 + tan2 θ+cot2 θ.
Advertisements
उत्तर
L.H.S : (sinθ+cosecθ)2 +(cosθ+secθ)2
=sin2θ + cosec2θ + 2 +cos2θ + sec2θ + 2 `[because sin θ = 1/(cosecθ) " and cos "θ = 1/ (secθ)]`
= sin2θ + cos2θ+1+cot2θ+1+tan2θ+4 `[because cosec^2θ+1+cot^2θ" and "sec^2 θ =1+ tan^2θ]`
=sin2θ+cos2θ+1+cot2θ+1+tan2θ+4 `[because cosec^2θ+1+cot^2θ " and" sec^2 θ=1 +tan^2θ]`
=1+1+1+4+tan2θ+cot2θ `[because cos^2θ+ sin^2θ=1]`
=7+ tan2θ+cot2θ
L.H.S-R.H.S
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities:
(i) (1 – sin2θ) sec2θ = 1
(ii) cos2θ (1 + tan2θ) = 1
If `x/a=y/b = z/c` show that `x^3/a^3 + y^3/b^3 + z^3/c^3 = (3xyz)/(abc)`.
Prove the following identities:
cosec4 A – cosec2 A = cot4 A + cot2 A
`(1+ cos theta - sin^2 theta )/(sin theta (1+ cos theta))= cot theta`
Show that none of the following is an identity:
`sin^2 theta + sin theta =2`
Prove that:
`"tan A"/(1 + "tan"^2 "A")^2 + "Cot A"/(1 + "Cot"^2 "A")^2 = "sin A cos A"`.
Prove the following identity :
`sqrt((1 - cosA)/(1 + cosA)) = sinA/(1 + cosA)`
Prove that `(sin 70°)/(cos 20°) + (cosec 20°)/(sec 70°) - 2 cos 70° xx cosec 20°` = 0.
tan (90 – θ) = ?
If tan θ = `x/y`, then cos θ is equal to ______.
