Advertisements
Advertisements
प्रश्न
If sin θ + sin2 θ = 1 show that: cos2 θ + cos4 θ = 1
Advertisements
उत्तर
sin θ + sin2 θ = 1 ......[Given]
∴ sin θ = 1 − sin2 θ
∴ sin θ = cos2 θ ......[∵ 1 − sin2 θ = cos2 θ]
∴ sin2 θ = cos4 θ ......[Squaring both the sides]
∴ 1 − cos2 θ = cos4 θ ......[∵ sin2 θ = 1 − cos2 θ]
∴ 1 = cos2 θ + cos4 θ
∴ cos2 θ + cos4 θ = 1
APPEARS IN
संबंधित प्रश्न
Prove that ` \frac{\sin \theta -\cos \theta +1}{\sin\theta +\cos \theta -1}=\frac{1}{\sec \theta -\tan \theta }` using the identity sec2 θ = 1 + tan2 θ.
Prove that `(sin theta)/(1-cottheta) + (cos theta)/(1 - tan theta) = cos theta + sin theta`
Evaluate without using trigonometric tables:
`cos^2 26^@ + cos 64^@ sin 26^@ + (tan 36^@)/(cot 54^@)`
Prove the following trigonometric identities.
`sqrt((1 - cos 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 trigonometric identities.
if `T_n = sin^n theta + cos^n theta`, prove that `(T_3 - T_5)/T_1 = (T_5 - T_7)/T_3`
Prove that:
(1 + tan A . tan B)2 + (tan A – tan B)2 = sec2 A sec2 B
Prove the following identities:
`sqrt((1 - cosA)/(1 + cosA)) = sinA/(1 + cosA)`
`sec theta (1- sin theta )( sec theta + tan theta )=1`
If tan A =` 5/12` , find the value of (sin A+ cos A) sec A.
Prove the following identity :
`sec^2A.cosec^2A = tan^2A + cot^2A + 2`
Prove that `(tan^2"A")/(tan^2 "A"-1) + (cosec^2"A")/(sec^2"A"-cosec^2"A") = (1)/(1-2 co^2 "A")`
If x = r sin θ cos Φ, y = r sin θ sin Φ and z = r cos θ, prove that x2 + y2 + z2 = r2.
If x = h + a cos θ, y = k + b sin θ.
Prove that `((x - h)/a)^2 + ((y - k)/b)^2 = 1`.
Prove the following identities: sec2 θ + cosec2 θ = sec2 θ cosec2 θ.
If sin θ + cos θ = a and sec θ + cosec θ = b , then the value of b(a2 – 1) is equal to
If x = a tan θ and y = b sec θ then
Prove that `costheta/(1 + sintheta) = (1 - sintheta)/(costheta)`
Prove that `"cot A"/(1 - tan "A") + "tan A"/(1 - cot"A")` = 1 + tan A + cot A = sec A . cosec A + 1
If cosec θ + cot θ = p, then prove that cos θ = `(p^2 - 1)/(p^2 + 1)`
