Advertisements
Advertisements
प्रश्न
The value of sin ( \[{45}^° + \theta) - \cos ( {45}^°- \theta)\] is equal to
विकल्प
2 cos \[\theta\]
0
2 sin \[\theta\]
1
उत्तर
We know that,
\[\sin\left( 90 - \theta \right) = \cos\theta\]
So,
\[\sin\left( 45°+ \theta \right) = \cos\left[ 90 - \left( 45° + \theta \right) \right] = \cos\left( 45° - \theta \right)\]
\[\therefore \sin\left( 45°+ \theta \right) - \cos\left( 45°- \theta \right)\]
\[ = \cos\left( 45° - \theta \right) - \cos\left( 45° - \theta \right)\]
\[ = 0\]
APPEARS IN
संबंधित प्रश्न
If cosθ + sinθ = √2 cosθ, show that cosθ – sinθ = √2 sinθ.
Prove the following trigonometric identities:
`(1 - cos^2 A) cosec^2 A = 1`
Prove the following trigonometric identities.
`tan theta + 1/tan theta = sec theta cosec theta`
Prove that `(sec theta - 1)/(sec theta + 1) = ((sin theta)/(1 + cos theta))^2`
Prove the following identities:
cosec A(1 + cos A) (cosec A – cot A) = 1
`(1-cos^2theta) sec^2 theta = tan^2 theta`
`sin theta / ((1+costheta))+((1+costheta))/sin theta=2cosectheta`
`(cos ec^theta + cot theta )/( cos ec theta - cot theta ) = (cosec theta + cot theta )^2 = 1+2 cot^2 theta + 2cosec theta cot theta`
If `sin theta = x , " write the value of cot "theta .`
Define an identity.
Write True' or False' and justify your answer the following :
The value of the expression \[\sin {80}^° - \cos {80}^°\]
Prove the following identity :
( 1 + cotθ - cosecθ) ( 1 + tanθ + secθ)
Prove the following identity :
`sin^4A + cos^4A = 1 - 2sin^2Acos^2A`
A moving boat is observed from the top of a 150 m high cliff moving away from the cliff. The angle of depression of the boat changes from 60° to 45° in 2 minutes. Find the speed of the boat in m/min.
Prove that `(sin θ tan θ)/(1 - cos θ) = 1 + sec θ.`
If cosθ + sinθ = `sqrt2` cosθ, show that cosθ - sinθ = `sqrt2` sinθ.
Prove that the following identities:
Sec A( 1 + sin A)( sec A - tan A) = 1.
Prove that `(sin^2theta)/(cos theta) + cos theta` = sec θ
Prove the following:
(sin α + cos α)(tan α + cot α) = sec α + cosec α
