Question

14. Prove that: Sin A (1 + tan A) + cos A (1 + cot A) = Sec A + Cosec A​

Answer 1

sin∅( 1 + tan ∅ ) + cos∅( 1 + cot ∅ ) = ( sec∅ + cosex∅ ) .

▶ Step-by-step explanation :-

Solving LHS :-)

∵sinθ(1+tanθ)+cosθ(1+cotθ)

=sinθ+sinθ×

cosθ

sinθ

+cosθ+cosθ×

sinθ

cosθ

.

=

sinθcosθ

sin

2

θcosθ+sin

2

θ+cos

2

θsinθ+cos

2

θ

=

cosθsinθ

(sin

3

θ+cos

3

θ)+(cosθsin

2

θ+cos

2

θsinθ)

.

=

cosθsinθ

(sinθ+cosθ)(sin

2

θ−sinθcosθ+cos

2

θ)+sinθcosθ(sinθ+cosθ)

.

=

cosθsinθ

(sinθ+cosθ)(sin

2

θ+cos

2

θ

−sinθcosθ

+sinθcosθ

)

.

=

cosθsinθ

(sinθ+cosθ)×1.

.

=

cosθ

sinθ

sinθ

+

cosθ

sinθ

cosθ

.

=

cosθ

1

+

sinθ

1

.

=secθ+cosecθ.