Advertisements
Advertisements
Question
Prove the following identities:
`sinA/(1 - cosA) - cotA = cosecA`
Advertisements
Solution
`sinA/(1 - cosA) - cotA`
= `sinA/(1 - cosA) - cosA/sinA`
= `(sin^2A - cosA + cos^2A)/((1 - cosA)sinA)`
= `(1 - cosA)/((1 - cosA)sinA)`
= `1/sinA`
= cosec A
APPEARS IN
RELATED QUESTIONS
If `x/a=y/b = z/c` show that `x^3/a^3 + y^3/b^3 + z^3/c^3 = (3xyz)/(abc)`.
Prove that `(tan^2 theta)/(sec theta - 1)^2 = (1 + cos theta)/(1 - cos theta)`
Prove the following trigonometric identities.
`(tan^2 A)/(1 + tan^2 A) + (cot^2 A)/(1 + cot^2 A) = 1`
Prove the following identities:
`(sinAtanA)/(1 - cosA) = 1 + secA`
Prove that:
`(cosecA - sinA)(secA - cosA) = 1/(tanA + cotA)`
`(sec theta -1 )/( sec theta +1) = ( sin ^2 theta)/( (1+ cos theta )^2)`
`(sin theta)/((sec theta + tan theta -1)) + cos theta/((cosec theta + cot theta -1))=1`
Write the value of `cosec^2 theta (1+ cos theta ) (1- cos theta).`
Prove the following identity :
`sin^2Acos^2B - cos^2Asin^2B = sin^2A - sin^2B`
If tan θ – sin2θ = cos2θ, then show that `sin^2θ = 1/2`.
