Evaluate-i Sin 90-Asin A - cos90-A cosAii sin2 35- - cos2 55-

(i)Given sin(90^∘ A)sin A cos(90^∘ A)cos A nbsp; = cos A sin A sin A cos A = 0 (ii)Given sin^2 35^∘ cos^2 55^∘ =sin^2 35^∘ cos^2(90^∘ 35^∘) =sin ...

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Byju's Answer

Standard IX

Mathematics

Complementary Trigonometric Ratios

Evaluate:i Si...

Question

Evaluate:
$(i) Sin (90^{\circ} - A) sin A - cos (90^{\circ} - A) cosA$
$(ii) s i n^{2} 35^{\circ} - c o s^{2} 55^{\circ}$

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Solution

$(i) Given sin (90^{\circ} - A) sin A - cos (90^{\circ} - A) cos A$
= cos A sin A - sin A cos A
= 0
$(i i) Given s i n^{2} 35^{\circ} - c o s^{2} 55^{\circ}$
$= s i n^{2} 35^{\circ} - c o s^{2} (90^{\circ} - 35^{\circ})$
$= s i n^{2} 35^{\circ} - s i n^{2} 35^{\circ}$
= 0

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Evaluate: (i) Sin (90∘−A)sin A - cos(90∘−A) cosA (ii) sin2 35∘−cos2 55∘

(i)Given sin(90∘−A)sin A - cos(90∘−A)cos A = cos A sin A - sin A cos A = 0 (ii)Given sin2 35∘−cos2 55∘ =sin2 35∘−cos2(90∘−35∘) =sin2 35∘−sin2 35∘ = 0

Evaluate:
$(i) Sin (90^{\circ} - A) sin A - cos (90^{\circ} - A) cosA$
$(ii) s i n^{2} 35^{\circ} - c o s^{2} 55^{\circ}$

$(i) Given sin (90^{\circ} - A) sin A - cos (90^{\circ} - A) cos A$
= cos A sin A - sin A cos A
= 0
$(i i) Given s i n^{2} 35^{\circ} - c o s^{2} 55^{\circ}$
$= s i n^{2} 35^{\circ} - c o s^{2} (90^{\circ} - 35^{\circ})$
$= s i n^{2} 35^{\circ} - s i n^{2} 35^{\circ}$
= 0