Question

Hi
Without using trigonometric tables, prove that:
cosec2 72° - tan2 18° = 1
solve pls..​

Answer 1

Answer:

cosec^2(72)-tan^2 (18)=1

Cosec^2 (90-18)-tan^2 (90-72)=1

Sec^2 (18)-tan^2 (18)=1

Hence,we know that [sec^2A-tan^2A=1],we get

Sec^2 (18)-tan^2 (18)=1

HENCE PROVED

Hope it helps...✌

Answer 2

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Consider cosec^2 72°- tan^2 18°

= cosec^2 72° - tan^2 (90 - 72)°

= cosec^2 72° - cot^2 72°

= 1

(∵1 + cot^2 θ = cosec^2 θ

⇒ cosec^2 θ - cot^2 θ = 1 )

Hence, proved.

Hope it helps you..♡