Question

prove that tan(45 + O/2) = tanO + sec O​

Answer 1

Answer:

$\huge\red{\boxed{\sf Answer}}$

tan (45+A/2) = (tan 45 - tan A/2)/(1 + tan 45 tan A/2)

→ (1- tan A/2)/(1+ tan A/2)

→(1- sin A/2/cos A/2)/(1+ sin A/2 / cos A/2)

→ (cos A/2 - sin A/2)/(cos A/2 + sin A/2)

→ ((cos A/2 - sin A/2)(cos A/2 + sin A/2))/(cos A/2 + sin A/2)²

→ (cos ² A/2 - sin ² A/2)/(cos² A/2 + sin ² A/2 + 2 sin A/2 cos A/2)

→(cos A)/(1+ sin A)

$\huge\red{\boxed{\sf (cos A)/(1+ sin A)}}$

Hence proved

Answer 2

Step-by-step explanation:

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