Question

show that 1/cosø‐cosø=tanø×sinø​

Answer 1

Answer:

shown

Explanation:

use the smiple algebra then use the identity of 1-(cosx)^2=(sinx)^2

and then simplify it

Answer 2

Explanation:

Given question :

$\mathrm {\frac{1}{cos \theta}- cos \theta = tan\theta \times sin\theta}$

Answer :

$LHS = \ \frac{1}{cos\theta} - cos \theta \\\\\implies \frac{1-cos^2\theta}{cos\theta} \\\\\implies \frac{sin^2\theta }{cos \theta} \ \ \ ------- \ \boxed {1 - cos^2 \theta = sin^2\theta }\\\\\implies \frac{sin\theta \ \times\ sin\theta}{cos\theta} \\\\\implies \frac {sin\theta}{cos\theta} \times sin\theta \\\\\implies tan\theta \times sin\theta\ \ \ -------- \ \ \boxed{\frac{sin\theta}{cos\theta} = tan\theta} \\\\\implies RHS \\\\\ \boxed{LHS=RHS}\\\\ \huge {\texttt {Hence Proved!}}$

Hope it helps

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