Advertisements
Advertisements
प्रश्न
Prove the following identities:
cosec A(1 + cos A) (cosec A – cot A) = 1
Advertisements
उत्तर
L.H.S. = cosec A(1 + cos A) (cosecA – cot A)
= `1/(sin A)(1 + cos A)(1/(sin A) - (cos A)/(sin A))`
`((1-cos A)/sin A)`
`1/sin A(1+cos A)((1-cos A)/sin A)`
`= ((1+ cos A)(1-cos A))/sin^2 A`
Apply the identity (1 + cosA) (1 − cosA) = 1 − cos2A
`= (1-cos^2A)/sin^2A`
`= sin^2A/sin^2A = 1`
cscA(1 + cosA) (cscA − cotA) = 1 proved
APPEARS IN
संबंधित प्रश्न
Prove that `(sec theta - 1)/(sec theta + 1) = ((sin theta)/(1 + cos theta))^2`
`sqrt((1+cos theta)/(1-cos theta)) + sqrt((1-cos theta )/(1+ cos theta )) = 2 cosec theta`
Write the value of `(1+ tan^2 theta ) ( 1+ sin theta ) ( 1- sin theta)`
If `cos theta = 2/3 , "write the value of" ((sec theta -1))/((sec theta +1))`
If sec2 θ (1 + sin θ) (1 − sin θ) = k, then find the value of k.
If sin θ + sin2 θ = 1, then cos2 θ + cos4 θ =
Prove that:
`(sin A + cos A)/(sin A - cos A) + (sin A - cos A)/(sin A + cos A) = 2/(2 sin^2 A - 1)`
Prove that 2(sin6A + cos6A) – 3(sin4A + cos4A) + 1 = 0.
If 1 + sin2α = 3 sinα cosα, then values of cot α are ______.
tan θ × `sqrt(1 - sin^2 θ)` is equal to:
