Advertisements
Advertisements
प्रश्न
Prove that `(cos(90^circ - A))/(sin A) = (sin(90^circ - A))/(cos A)`.
Advertisements
उत्तर
L.H.S. = `(cos(90^circ - A))/(sin A)`
= `(sin A)/(sin A)`
= 1
R.H.S. = `(sin(90^circ - A))/(cos A)`
= `(cos A)/(cos A)`
= 1
∴ L.H.S. = R.H.S.
APPEARS IN
संबंधित प्रश्न
Prove the following identities:
`(i) (sinθ + cosecθ)^2 + (cosθ + secθ)^2 = 7 + tan^2 θ + cot^2 θ`
`(ii) (sinθ + secθ)^2 + (cosθ + cosecθ)^2 = (1 + secθ cosecθ)^2`
`(iii) sec^4 θ– sec^2 θ = tan^4 θ + tan^2 θ`
Express the ratios cos A, tan A and sec A in terms of sin A.
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(sin theta-2sin^3theta)/(2cos^3theta -costheta) = tan theta`
Prove the following trigonometric identities:
`sin theta/(1 - cos theta) = cosec theta + cot theta`
Prove the following trigonometric identities.
`(1 + cos theta - sin^2 theta)/(sin theta (1 + cos theta)) = cot theta`
Prove the following identities:
cot2 A – cos2 A = cos2 A . cot2 A
Prove the following identities:
(cos A + sin A)2 + (cos A – sin A)2 = 2
Prove the following identities:
`sinA/(1 - cosA) - cotA = cosecA`
Prove that:
`sqrt(sec^2A + cosec^2A) = tanA + cotA`
`sin^6 theta + cos^6 theta =1 -3 sin^2 theta cos^2 theta`
Prove the following identities:
`(cos theta "cosec" theta - sin theta sec theta )/(cos theta + sin theta) = "cosec" theta - sec theta`
`((sin A- sin B ))/(( cos A + cos B ))+ (( cos A - cos B ))/(( sinA + sin B ))=0`
Write 'True' or 'False' and justify your answer in the following:
The value of \[\sin \theta\] is \[x + \frac{1}{x}\], where 'x' is a positive real number.
Prove the following identity :
`(cosecA - sinA)(secA - cosA)(tanA + cotA) = 1`
If x = r sin θ cos Φ, y = r sin θ sin Φ and z = r cos θ, prove that x2 + y2 + z2 = r2.
Prove the following identities:
`1/(sin θ + cos θ) + 1/(sin θ - cos θ) = (2sin θ)/(1 - 2 cos^2 θ)`.
Prove that: `1/(cosec"A" - cot"A") - 1/sin"A" = 1/sin"A" - 1/(cosec"A" + cot"A")`
If `(cos alpha)/(cos beta)` = m and `(cos alpha)/(sin beta)` = n, then prove that (m2 + n2) cos2 β = n2
If sin θ + sin2 θ = 1 show that: cos2 θ + cos4 θ = 1
If `sec θ = 41/40`, then find values of sin θ, cot θ, cosec θ.
