Question

sin 35 cos 55+ cos 35 sin 55/cosec²10- tan²80

Answer 1

Trigonometric Problem

Step-by-step explanation:

$\therefore \frac{sin35^{\circ}\:cos55^{\circ}+cos35^{\circ}\:sin55^{\circ}}{cosec^{2}10^{\circ}-tan^{2}80^{\circ}}$

$=\frac{sin(35^{\circ}+55^{\circ})}{cosec^{2}10^{\circ}-tan^{2}(90^{\circ}-10^{\circ})}$

$=\frac{sin90^{\circ}}{cosec^{2}10^{\circ}-cot^{2}10^{\circ}}$

$=\frac{1}{1}$

$=1$

$\Rightarrow \boxed{\frac{sin35^{\circ}\:cos55^{\circ}+cos35^{\circ}\:sin55^{\circ}}{cosec^{2}10^{\circ}-tan^{2}80^{\circ}}=1}$

Rules used in solving the problem:

$1.\:sinA\:cosB+cosA\:sinB=sin(A+B)$

$2.\:tan(90^{\circ}-A)=cotA$

$3.\:cosec^{2}A-cot^{2}A=1$

Note:

The most important thing in solving trigonometric problems is to use its identities or formulas appropriately.

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