Question

Sin theta/cos theta+cos theta/sin theta = sec theta cosec theta

Answer 1

Answer:

Sec theta × cosec theta

Step-by-step explanation:

LHS

$\frac{sin \: theta}{cos \: theta} + \frac{cos \: theta}{sin \: theta} \\ \\ = \frac{ {sin}^{2} \: theta \: + {cos}^{2} theta }{cos \: theta \times \: sin \: theta} - - taking \: out \: lcm \\ \\ = \frac{1}{cos \: theta \: \times sin \: theta} \\ \\ = \frac{1}{cos \: theta} \times \frac{1}{sin \: theta} \\ \\ = sec \: theta \: cosec \: theta \\ \\ =</u></strong><strong><u> </u></strong><strong><u>RHS</u></strong><strong><u>$

Answer 2

Answer:

LHS: Sin theta/cos theta+cos theta/sin theta

(sin^2theta+cos^2theta)/cos theta×sin theta

1/cos theta sin theta

1/cos theta×1/sin theta

sec theta.cosec theta=RHS