Question

Complete the following activity to prove cot 0 + tan @ = tosec 0 - sec e. LHS = cot 0 + tan 0 cos e + sin 0 cos 0 e + sin o x cos 0 sin o x cos e 1 = = cosec 0 X sec 0 RHS​

Answer 1

Answer:

We have,

LHS =

sinθcosθ

tanθ−cotθ

=

sinθcosθ

cosθ

sinθ

−

sinθ

cosθ

=

cosθsinθ

sinθcosθ

sin

2

θ−cos

2

θ

⇒ LHS =

sin

2

θcos

2

θ

sin

2

θ−cos

2

θ

⇒ LHS =

sin

2

θcos

2

θ

sin

2

θ

−

sin

2

θcos

2

θ

cos

2

θ

⇒ LHS =

cos

2

θ

1

−

sin

2

θ

1

⇒ LHS = sec

2

θ−cosec

2

θ=(1+tan

2

θ)−(1+cot

2

θ)=tan

2

θ−cot

2

θ=RHS.