Question

tantheta /1+tan square theta=sintheta .cos theta
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Answer 1

Solution :-

On taking LHS

tan θ / ( 1 + tan² θ)

We know that

sec² θ - tan² θ = 1

Now,

tan θ / sec² θ

= (sin θ/cos θ)/sec² θ

Since , tan θ = sin θ / cos θ

= sin θ / ( cos θ × sec² θ)

= sin θ / ( cos θ / cos² θ)

Since, sec θ = 1 / cos θ

= sin θ / (1/cos θ)

= sin θ ×( cos θ / 1)

= sin θ × cos θ

= RHS

Therefore, LHS = RHS

tan θ / ( 1 + tan² θ) = sin θ × cos θ

Hence, Proved.

Used formulae:-

→ sec² θ - tan² θ = 1

→ tan θ = sin θ / cos θ

→ sec θ = 1 / cos θ

Answer 2

refer the given attachment