# If Sin (A+B) = Sin a Cos B + Cos a Sin B and Cos (A-b) = Cos a Cos B + Sin a Sin B (I) Sin (750) (Ii) Cos (150) - Mathematics

If sin (A+B) = sin A cos B + cos A sin B and cos (A-B) = cos A cos B + sin A sin B
(i) sin (750)
(ii) cos (150

#### Solution

Let A = 450 and B = 300
(i) As, sin(A + B) = sin A cos B + cos A sin B
⇒ sin (450 + 300)  = sin 450 cos 300 + cos 450 sin 300

⇒ sin (75^0) = 1/sqrt(2) xx sqrt(3)/2 + 1/sqrt(2) xx1/2

⇒ sin (75^0) = sqrt(3)/(2sqrt(2)) + 1/(2sqrt(2))

∴ sin (75^0) = (sqrt(3) +1)/(2 sqrt(2))

ii) As, cos (A – B) = cos A cos B + sin A sin B
⇒ cos (450 – 300) = cos 450 cos 300 + sin 450 sin 30

⇒ cos (15^0) = 1/sqrt(2) xx sqrt(3)/2 + 1/sqrt(2) xx1/2

⇒ cos (15^0) = sqrt(3)/(2sqrt(2)) + 1/(2sqrt(2))

∴ cos (15^0)=(sqrt(3)+1)/(2sqrt(2))

Disclaimer: cos 150 can also be written by taking A = 600 and B = 450

Concept: Trigonometric Ratios and Its Reciprocal
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#### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 6 T-Ratios of some particular angles
Exercises | Q 27
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