Advertisements
Advertisements
प्रश्न
Prove the following identities:
`secA/(secA + 1) + secA/(secA - 1) = 2cosec^2A`
उत्तर
L.H.S. = `secA/(secA + 1) + secA/(secA - 1)`
= `(sec^2A - secA + sec^2A + secA)/(sec^2A - 1`
= `(2sec^2A)/tan^2A` ...(∵ sec2 A – 1 = tan2 A)
= `(2/cos^2A)/(sin^2A/cos^2A)`
= `2/sin^2A`
= 2 cosec2 A = R.H.S.
APPEARS IN
संबंधित प्रश्न
If x cos A + y sin A = m and x sin A – y cos A = n, then prove that : x2 + y2 = m2 + n2
Prove the following identities:
`(sinA - cosA + 1)/(sinA + cosA - 1) = cosA/(1 - sinA)`
Prove the following identities:
`cot^2A((secA - 1)/(1 + sinA)) + sec^2A((sinA - 1)/(1 + secA)) = 0`
`cos^2 theta /((1 tan theta))+ sin ^3 theta/((sin theta - cos theta))=(1+sin theta cos theta)`
`(sin theta+1-cos theta)/(cos theta-1+sin theta) = (1+ sin theta)/(cos theta)`
`{1/((sec^2 theta- cos^2 theta))+ 1/((cosec^2 theta - sin^2 theta))} ( sin^2 theta cos^2 theta) = (1- sin^2 theta cos ^2 theta)/(2+ sin^2 theta cos^2 theta)`
If ` cot A= 4/3 and (A+ B) = 90° ` ,what is the value of tan B?
Prove the following identity :
`sec^2A.cosec^2A = tan^2A + cot^2A + 2`
Prove the following identity :
`(1 + cosA)/(1 - cosA) = tan^2A/(secA - 1)^2`
Prove that `(tan(90 - theta) + cot(90 - theta))/("cosec" theta)` = sec θ
