Question

If sin theta = cos theta , then find the value of
2tan theta + cos² theta​

Answer 1

Question

If sin theta = cos theta , then find the value of2tan theta + cos² theta

Solutions

cosФ = sin(90° - Ф)

sinФ = cosФ

⇒ sinФ = sin(90° - Ф)

Dividing both sides by Sin

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⇒ Ф = 90° - Ф

⇒ Ф + Ф = 90° - Ф + Ф

⇒ 2Ф = 90°

⇒ Ф = 90°/2

⇒ Ф = 45°

2 tanФ + cos²Ф

= 2 × tan 45 ° + cos²45°

= 2 × 1 + (1/√2)²

= 2 + (1/2)

add them :-

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= 4/2 + 1/2

= 5/2

therefore the answer is 5/2

Thanks