Question

EXPRESS THE FOLLOWING AS SUM OR DIFFERENCE OF TRIGONOMETRIC RATIOS (i) 2sin32°.cos28° (ii) 2cos 78°.sin42° (iii) 2cos 54°.sin66°
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Answer 1

Step-by-step explanation:

(1)Given that :-2sin32°.cos28°

We know that

Sin(A+B)+Sin(A-B)= 2 SinA CosB

=>2sin32°.cos28°

Here, A =32° and B=28°

=>Sin(32°+28°)+Sin(32°-28°)

=>Sin60°+Sin4°(or)

=>√3/2+sin4°

(2)2cos 78°.sin42°

We know that:-

Sin(A+B)-Sin(A-B)=2CosASinB

now , 2Cos 78° Sin42°

here, A=78° and B=42°

=>Sin(78°+42°)-Sin(78°-42°)

=>Sin120°-Sin36° ( or)

=>Sin(90+30)-Sin36°

=>Cos30°-Sin36°

=>√3/2-Sin36°. (sin(90+A)=cosA)

(3)2Cos54°Sin66°=2Sin66°Cos54°

We know that:-

Sin(A+B)+Sin(A-B)= 2SinACosB

Here, A=66° and B =54°

now,

=>2Cos 54° Sin66°

=>2Sin66°Cos54°

=>Sin(66°+54°)+Sin(66°-54°)

=>Sin120°+Sin12° (or)

=>Sin(90°+30°)+Sin12°

=>Cos30°+Sin12° (or)

=>√3/2 + Sin12°. (Sin(90+A)=CosA)

Answer 2

Answer:

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