Question

cos(A-B) - cos(A+B) =​

Answer 1

Answer: cos (A+B)+cos (A-B)

= cos A cos B - sin A sin B + cos A cos B + sin A sin B

= 2 cos A cos B.

Answer 2

★ Solution :-

We need to find ,

cos(A - B) - cos(A + B)

As we know that ,

• cos(A - B) = cosAcosB + sinAsinB
• cos(A + B) = cosAcosB - sinAsinB

Substituting the values we have,

→ cosAcosB + sinAsinB - [ cosAcosB - sinAsinB ]

→ cosAcosB + sinAsinB - cosAcosB + sinAsinB

→ sinAsinB + sinAsinB

→ cos(A - B) - cos(A + B) = 2sinAsinB

Hence , cos(A - B) - cos(A + B) = 2sinAsinB

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★ More information :-

Trigonometric identities

• sin²A + cos²A = 1
• sec²A - tan²A = 1
• cosec²A - cot²A = 1

Trigonometric formulae

• tanA = sinA/cosA
• cotA = cosA/sinA
• sin2A = 2sinAcosA
• cos2A = 1 - 2cos²A or sin²A - cos²A
• tan2A = 2tanA/1 - tan²A
• sin(A + B) = sinAcosB + cosAsinB
• sin(A - B ) = sinAcosB - cosAsinB
• cos(A + B) = cosAcosB - sinAsinB
• cos(A - B) = cosAcosB + sinAsinB