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express cos θ-sinθ as a cosine angle please give me total solution and also plz tell me why we have to divide and multiply with root2

express cosθ-sinθ as a cosine angle
please give me total solution
and also plz tell me why we have to divide and multiply with root2
 

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Grade:11

1 Answers

Balwant Mittal
28 Points
4 years ago
Multiply and divided √2 (because it's value where angle of both sine and cosine are same so that we can make a formula of cos x cosy- sinx Sony)
√2(1/√2 cosx- 1/√2 sinx)
= √2( cos(45°+X)
 
( because cos a cosb - sin a sin b = cos(a+b))
1/√2 =cos 45 = sin 45

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