1 of 1

+ cos²A

1

+ 2

+ cosec²A

+ 2

+ sec²A

Q.

(sinA + cosecA)² + (cosA + secA)² = 7 + tan²A + cot²A

Soln.

L.H.S.

=

(sinA

+ cosecA)²

+ (cosA

+ secA)²

=

sin²A

+ 2

+ cosec²A

+ cos²A

+ 2

+ sec²A

=

sin²A

+ cos²A

+ 2

+ cosec²A

+ 2

+ sec²A

∴

sinA =

1

cosecA

and

cosA =

1

secA

=

sin²A

+ 2

+ cosec²A

+ 2

+ sec²A

=

5

+ cosec²A

+ sec²A

=

5

+ 1

+ cot²A

+ 1

+ tan²A

=

7

+ tan²A

+ cot²A

=

R.H.S.

(sinA + cosecA)² + (cosA + secA)² = 7 + tan²A + cot²A

∴

.cosecA

.secA

=

sin²A

+2.

+ cosec²A

+ cos²A

+2.

+ sec²A

.cosecA

.secA

1

cosecA

1

secA

Lets start with the

more complicated side

Identify the algebraic expression

=

Expansion ??

a² + 2ab + b²

sinA

cosA

=

sin²A + cos²A =

??

1

We will convert cosec and

sec into cot

and tan

cosec²A =

??

1 + cot²A

sec²A =

??

1 + tan²A

i.e. L.H.S.

We want tan and cot

in the R.H.S.

a

b

+

(

)²

a

b

+

(

)²

Ex. 8.4 Q.5(viii)