Advertisements
Advertisements
प्रश्न
If sin θ − cos θ = 0 then the value of sin4θ + cos4θ
पर्याय
1
\[- 1\]
\[\frac{1}{2}\]
\[\frac{1}{4}\]
Advertisements
उत्तर
`bb(1/2)`
Explanation:
It is given that,
\[\sin\theta - \cos\theta = 0\]
\[ \Rightarrow \sin\theta = \cos\theta\]
\[ \Rightarrow \frac{\sin\theta}{\cos\theta} = 1\]
\[ \Rightarrow \tan\theta = 1\]
\[ \Rightarrow \tan\theta = \tan45°\]
\[ \Rightarrow \theta = 45°\]
\[\therefore \sin^4 \theta + \cos^4 \theta\]
\[ = \sin^4 45° + \cos^4 45°\]
\[ = \left( \frac{1}{\sqrt{2}} \right)^4 + \left( \frac{1}{\sqrt{2}} \right)^4 \]
\[ = \frac{1}{4} + \frac{1}{4}\]
\[ = \frac{1}{2}\]
APPEARS IN
संबंधित प्रश्न
(secA + tanA) (1 − sinA) = ______.
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(tan theta)/(1-cot theta) + (cot theta)/(1-tan theta) = 1+secthetacosectheta`
[Hint: Write the expression in terms of sinθ and cosθ]
if `cos theta = 5/13` where `theta` is an acute angle. Find the value of `sin theta`
Show that `sqrt((1-cos A)/(1 + cos A)) = sinA/(1 + cosA)`
Prove the following trigonometric identities.
tan2θ cos2θ = 1 − cos2θ
Prove the following trigonometric identities.
`sin^2 A + 1/(1 + tan^2 A) = 1`
Prove the following trigonometric identities.
`(cos^2 theta)/sin theta - cosec theta + sin theta = 0`
Prove the following identities:
`sqrt((1 - cosA)/(1 + cosA)) = sinA/(1 + cosA)`
If `cos theta = 7/25 , "write the value of" ( tan theta + cot theta).`
Prove that:
`"tanθ"/("secθ" – 1) = (tanθ + secθ + 1)/(tanθ + secθ - 1)`
If cosec θ − cot θ = α, write the value of cosec θ + cot α.
If \[\sin \theta = \frac{1}{3}\] then find the value of 2cot2 θ + 2.
Prove the following identity :
`(cosA + sinA)^2 + (cosA - sinA)^2 = 2`
prove that `1/(1 + cos(90^circ - A)) + 1/(1 - cos(90^circ - A)) = 2cosec^2(90^circ - A)`
Prove that `((1 + sin θ - cos θ)/( 1 + sin θ + cos θ))^2 = (1 - cos θ)/(1 + cos θ)`.
Prove that : `tan"A"/(1 - cot"A") + cot"A"/(1 - tan"A") = sec"A".cosec"A" + 1`.
Prove the following identities.
tan4 θ + tan2 θ = sec4 θ – sec2 θ
Prove that `(1 + sec A)/(sec A) = (sin^2A)/(1 - cos A)`.
Prove that `sec^2A - "cosec"^2A = (2sin^2A - 1)/(sin^2A *cos^2A)`.
Prove that sin θ (1 – tan θ) – cos θ (1 – cot θ) = cosec θ – sec θ.
