sin2 a + cos2 (a + b) + 2 sin a sin b cos(a + b) is independent of

Question

Asked on March 26, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

Accepted Answer · 2026-03-26T12:49:42.465Z

Step 1: Simplify the given expression using trigonometric identities. The given expression is: E = ^2 + ^2( + ) + 2 ( + ) We use the product-to-sum identity 2 A B = (A-B) - (A+B). Substitute A = and B = : 2 = ( - ) - ( + ) Substitute this into the expression for E: E = ^2 + ^2( + ) + (( - ) - ( + ))( + ) Distribute ( + ) in the last term: E = ^2 + ^2( + ) + ( - )( + ) - ^2( + ) The terms ^2( + ) and -^2( + ) cancel out: E = ^2 + ( - )( + ) Step 2: Simplify the product of cosines. We use the product-to-sum identity 2 A B = (A+B) + (A-B). Substitute A = - and B = + : ( - )( + ) = (1)/(2)[(( - ) + ( + )) + (( - ) - ( + ))] ( - )\

Accepted Answer · 2026-03-26T12:49:42.465Z

Step 1: Simplify the given expression using trigonometric identities. The given expression is: E = ^2 + ^2( + ) + 2 ( + ) We use the product-to-sum identity 2 A B = (A-B) - (A+B). Substitute A = and B = : 2 = ( - ) - ( + ) Substitute this into the expression for E: E = ^2 + ^2( + ) + (( - ) - ( + ))( + ) Distribute ( + ) in the last term: E = ^2 + ^2( + ) + ( - )( + ) - ^2( + ) The terms ^2( + ) and -^2( + ) cancel out: E = ^2 + ( - )( + ) Step 2: Simplify the product of cosines. We use the product-to-sum identity 2 A B = (A+B) + (A-B). Substitute A = - and B = + : ( - )( + ) = (1)/(2)[(( - ) + ( + )) + (( - ) - ( + ))] ( - )\

sin2 a + cos2 (a + b) + 2 sin a sin b cos(a + b) is independent of

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sin2 a + cos2 (a + b) + 2 sin a sin b cos(a + b) is independent of

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