cos^2 ⁡5^ - cos^2 ⁡15^ - sin^2 ⁡15^ + sin^2 ⁡35^ + cos ⁡15^ sin ⁡15^ - cos ⁡5^ sin ⁡35^ =

Question

Accepted Answer

Correct answer: A. (a) Given, cos^2 ⁡5^ - cos^2 ⁡15^ - sin^2 ⁡15^ + sin^2 ⁡35^ + cos ⁡15^ sin ⁡15^ - cos ⁡5^ sin ⁡35^ After rearranging the terms = cos ⁡5^ ( cos ⁡5^ - sin ⁡35^ )- cos ⁡15^ (( cos ⁡15^ - sin ⁡15^ )+ sin^2 ⁡35^ - sin^2 ⁡15^ = cos ⁡5^ ( cos ⁡5^ - cos ⁡55^ )- cos ⁡15^ ( cos ⁡15^ - cos ⁡75^ )+ sin ⁡50^ sin ⁡20^ =- cos ⁡15^ 2+ cos ⁡5^ sin ⁡25^ + sin ⁡50^ sin ⁡20^ =- cos ⁡15^ 2+ 12( cos ⁡70^ + cos ⁡60^ + cos ⁡30^ - cos ⁡70^ ) =- cos ⁡15^ 2+ 12 (2 cos ⁡45^ cos ⁡15^ ) =- cos ⁡15^ 2+ cos ⁡15^ 2=0 Hence, option (a) is correct.

$cos^{2} 5^{\circ} - cos^{2} 15^{\circ} - sin^{2} 15^{\circ} + sin^{2} 35^{\circ} + cos 15^{\circ} sin 15^{\circ} - cos 5^{\circ} sin 35^{\circ} =$

Solution

More Trigonometric Ratios & Identities PYQs