Advertisements
Advertisements
प्रश्न
If sinA + cosA = `sqrt(2)` , prove that sinAcosA = `1/2`
Advertisements
उत्तर
We Know , `(sinA + cosA)^2 = sin^2A + cos^2A + 2sinA.cosA`
Given , (sinA + cosA) = `sqrt(2)`
⇒ 2 = 1 + 2sinA.cosA
⇒ 2sinA.cosA = 1
⇒ sinA.cosA = `1/2`
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`(1 + cos A)/sin A = sin A/(1 - cos A)`
Prove the following identities:
(cosec A – sin A) (sec A – cos A) (tan A + cot A) = 1
`(sin theta+1-cos theta)/(cos theta-1+sin theta) = (1+ sin theta)/(cos theta)`
Write the value of tan1° tan 2° ........ tan 89° .
What is the value of (1 + cot2 θ) sin2 θ?
Prove the following identities:
`(tan"A"+tan"B")/(cot"A"+cot"B")=tan"A"tan"B"`
Prove that `tan A/(1 + tan^2 A)^2 + cot A/(1 + cot^2 A)^2 = sin A.cos A`
a cot θ + b cosec θ = p and b cot θ + a cosec θ = q then p2 – q2 is equal to
Let α, β be such that π < α – β < 3π. If sin α + sin β = `-21/65` and cos α + cos β = `-27/65`, then the value of `cos (α - β)/2` is ______.
sec θ when expressed in term of cot θ, is equal to ______.
