यदि `sin21^(@)=(x)/(y)` है तो `sec21^(@)-sin69^(@)` किसके बराबर होगा?)

Options

A. `(x^(2))/(y(y^(2)-x^(2))`
B. `(y^(2))/(x(y^(2)-x^(2))`
C. `(x^(2))/(y(x^(2)-y^(2))`
D. `(y^(2))/(x(x^(2)-y^(2))`

Answer

a

Explanation

In `DeltaABC 1^(@)=(x)/(y)`
AB=x
A C=y
`BC=sqrt(y^(2)-x^(2))`
`rArr sec21^(@)-sin69^(@)`
`rArr(AC)/(BC)=(BC)/(AC)`
`rArr((AC)^(2)-(BC)^(2))/((BC)(AC ))=(y^(2)-(sqrt( (y^(2)- x ^( 2))))^(2))/(ysqrt(y ^(2)-x^(2)))`
`rArr(y^(2)-y^(2)+x^(2))/(ysqrt(y^(2)-x^(2)))=(x^(2))/(ysqrt(y^(2)-x^(2)))`