Question

Solve: sin(90 - 0)* cos(90 - 0) * tan(90 - 0)​

Answer 1

Answer:

Step-by-step explanation:

$= > \sin(90 -</strong><strong>\</strong><strong>t</strong><strong>h</strong><strong>e</strong><strong>t</strong><strong>a</strong><strong> ) \times \cos(90 - </strong><strong>\</strong><strong>t</strong><strong>h</strong><strong>e</strong><strong>t</strong><strong>a</strong><strong>) \times \tan(90 - </strong><strong>theta</strong><strong>) \\ \\ = > \cos(</strong><strong>\</strong><strong>t</strong><strong>h</strong><strong>e</strong><strong>t</strong><strong>a</strong><strong>) \times \sin(</strong><strong>\</strong><strong>t</strong><strong>h</strong><strong>e</strong><strong>t</strong><strong>a</strong><strong>) \times \cot(</strong><strong>\</strong><strong>theta</strong><strong>) \\ \\ = ></strong><strong> </strong><strong>\cos(\theta) \times \sin(\theta)</strong><strong> </strong><strong>\</strong><strong>t</strong><strong>i</strong><strong>m</strong><strong>e</strong><strong>s</strong><strong> </strong><strong>\</strong><strong>frac</strong><strong>{</strong><strong>\</strong><strong>s</strong><strong>in</strong><strong>(</strong><strong>\</strong><strong>t</strong><strong>h</strong><strong>e</strong><strong>t</strong><strong>a</strong><strong>)</strong><strong>}</strong><strong>{</strong><strong>\</strong><strong>c</strong><strong>o</strong><strong>s</strong><strong>(</strong><strong>\</strong><strong>t</strong><strong>h</strong><strong>e</strong><strong>t</strong><strong>a</strong><strong>)</strong><strong>}</strong><strong>\</strong><strong>\</strong><strong> </strong><strong>\</strong><strong>\</strong><strong> </strong><strong>=</strong><strong>></strong><strong> </strong><strong>\</strong><strong>c</strong><strong>o</strong><strong>s</strong><strong>(</strong><strong>\</strong><strong>t</strong><strong>h</strong><strong>e</strong><strong>t</strong><strong>a</strong><strong>)</strong><strong>$

Answer 2

sin(90-∅) ×cos(90-∅) ×tan(90-∅)

→ cos ∅×sin∅×cot ∅

→ cos∅×sin∅×cos∅/sin∅

→ cos ∅×cos∅

→ cos²∅

Trigonometric identities used here :

(1) sin(90-∅) =cos∅

(2) cos(90-∅) =sin∅

(3) tan (90-∅) =cot∅

(4) cot∅= cos∅/sin∅