Question

cosectheta +cottheta =p,prove that costheta =p^2-1/p^2+1

Answer 1

Taking theta as @
cosec@ + cot@ = p
p^2-1/ p^2+1 = (cosec@ + cot@)^2 -1 / (cosec@ + cot@)^2 +1
= cosec^2@ + cot^2@ + 2cosec@cot@ -1 / cosec@^2 + cot^2@ + 2cosec@cot@ +1
=cot^2@ + cot^2@ + 2cosec@cot@ / cosec^2@ + cosec^2@ + 2cosec@cot@
=2cot^2@ + 2cosec@cot@/ 2cosec^2@ + 2cosec@cot@
= 2cot@( cot@ + cosec@) /2cosec@ (cosec@ + cot@)
=2cot@/ 2 cosec@
= cos@/sin@ × sin@
= cos@
= cos theta
Hence Proved!!