Question

Sin (1+tan)+cos (1+cot)=(sec+cosec)

Answer 1

sin(1+sin/cos)+cos(1+cos/sin)
sin(cos+sin/cos)+cos(sin+cos/sin)
(sin+cos)(sin/cos+cos/sin)
(sin+cos)/(sincos)
1/cos+1/sin
sec+cosec

Answer 2

$<i> <b><marquee>Here's your answer</marquee></b></i>$

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

Squaring the term
sin² + cos² [(1+tan²)+(1+cot²)]

(sec² + cosec²)

Removing the square
sec + cosec

$<b><marquee>OR</marquee></b>$

sin × 1+$\frac{sin}{cos}$ + cos × 1+$\frac{cos}{sin}$

=>sin ×$\frac{cos+sin}{cos}$ + cos $\frac{sin+cos}{sin}$

=>sin+cos$\frac{cos(sq)+sin(sq)}{cos×sin}$

=>$\frac{sin + cos}{cos× sin}$

=>$\frac{1}{cos}$+$\frac{1}{sin}$

sec + cosec

Hope it helps you :)

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