Question

Prove that sin θ (1 + tan θ) + cos θ (1 + cot θ) = sec θ + cosec θ.

Answer 1

Answer:

Step-by-step explanation:

sin θ ( 1 + tan θ ) + cos θ ( 1 + cot θ )

sin θ ( 1 + sin θ / cos θ ) + cos θ ( 1 + cos θ / sin θ )

sin θ ( cos θ + sin θ ) / cos θ + cos θ ( sin θ + cos θ ) / sin θ

( cos θ + sin θ ) ( tan θ + cot θ )

( cos θ + sin θ ) ( sin² θ + cos²θ ) / ( sin θ cos θ )

( cos θ + sin θ ) / ( sin θ cos θ ) since sin² θ + cos²θ = 1

[ cos θ / ( sin θ cos θ ) ] + [ sin θ / ( sin θ cos θ ) ]

1 / sin θ + 1 / cos θ

cosec θ + sec θ

Answer 2

the answer is in the above pictures

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