Question

Prove that sin(90-a)/cosec(90-a)- cot(90-a)=1+sina
​

Answer 1

cos(90−A)=sin(A);

sin(90−A)=cos(A);

tan(90−A)=cot(A)

cot(A) = $\frac{cos(A)}{sin(A)}$

_______________________________

LHS

$\frac{cos(90-A)sin(90-a)}{tan(90-a)}$

=

$\frac{sin(A)cos(A)}{cot(A)}$

_______________________________

$\frac{sin(A)cos(A)}{cot(A)}$

=

$\frac{sin(A)cos(A)sin(A)}{cos(A)}$

_______________________________

$\frac{sin(A)cos(A)sin(A)}{cos(A)}$

=

sin(A) sin(A) = sin²(A)

RHS

sin²(A)

LHS = RHS

Hence Proved☑

Answer 2

Answer:

cos(90−A)=sin(A);

sin(90−A)=cos(A);

tan(90−A)=cot(A)

cot(A) = \{cos(A)}{sin(A)}

sin(A)

cos(A)

_______________________________

LHS

\frac{cos(90-A)sin(90-a)}{tan(90-a)}

tan(90−a)

cos(90−A)sin(90−a)

=

\frac{sin(A)cos(A)}{cot(A)}

cot(A)

sin(A)cos(A)

_______________________________

\frac{sin(A)cos(A)}{cot(A)}

cot(A)

sin(A)cos(A)

=

\frac{sin(A)cos(A)sin(A)}{cos(A)}

cos(A)

sin(A)cos(A)sin(A)

_______________________________

\frac{sin(A)cos(A)sin(A)}{cos(A)}

cos(A)

sin(A)cos(A)sin(A)

=

sin(A) sin(A) = sin²(A)

RHS

sin²(A)

LHS = RHS

Hence Proved☑