Advertisements
Advertisements
प्रश्न
Factorize: sin3θ + cos3θ
Hence, prove the following identity:
`(sin^3θ + cos^3θ)/(sin θ + cos θ) + sin θ cos θ = 1`
उत्तर
sin3θ + cos3θ
=(sin θ + cos θ)(sin2θ + cos2 – sin θ cos θ)
= (sin θ + cos θ)(1 – sin θ cos θ). ...(i)
L.H.S = `(sin^3θ + cos^3θ)/(sinθ + cosθ) + sinθcosθ`
= `((sinθ + cosθ)(1 - sinθcosθ))/((sinθ + cosθ)) + sinθcosθ` ...(From(i))
= 1 – sin θ cos θ + sin θ + cos θ
= 1
= R.H.S.
APPEARS IN
संबंधित प्रश्न
Prove that `\frac{\sin \theta -\cos \theta }{\sin \theta +\cos \theta }+\frac{\sin\theta +\cos \theta }{\sin \theta -\cos \theta }=\frac{2}{2\sin^{2}\theta -1}`
Prove the following trigonometric identities.
`(1 - cos theta)/sin theta = sin theta/(1 + cos theta)`
Prove the following identities:
`(sinA + cosA)/(sinA - cosA) + (sinA - cosA)/(sinA + cosA) = 2/(2sin^2A - 1)`
Prove that:
`1/(sinA - cosA) - 1/(sinA + cosA) = (2cosA)/(2sin^2A - 1)`
` (sin theta - cos theta) / ( sin theta + cos theta ) + ( sin theta + cos theta ) / ( sin theta - cos theta ) = 2/ ((2 sin^2 theta -1))`
Write the value of tan1° tan 2° ........ tan 89° .
If `secθ = 25/7 ` then find tanθ.
If \[\sin \theta = \frac{4}{5}\] what is the value of cotθ + cosecθ?
`(sin A)/(1 + cos A) + (1 + cos A)/(sin A)` = 2 cosec A
To prove cot θ + tan θ = cosec θ × sec θ, complete the activity given below.
Activity:
L.H.S = `square`
= `square/sintheta + sintheta/costheta`
= `(cos^2theta + sin^2theta)/square`
= `1/(sintheta*costheta)` ......`[cos^2theta + sin^2theta = square]`
= `1/sintheta xx 1/square`
= `square`
= R.H.S
