Solve the problem 2....
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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 ( Hence Proved )
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 ( Hence Proved )
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