Simplify (sin θ − cos θ)2 + (sin θ + cos θ)2

Answer in simplified form is:

(sinФ - cosФ)² + (sinФ + cosФ)² = 2

Step-by-step explanation:

Given,

(sinФ - cosФ)² + (sinФ + cosФ)²

This can be simplified as:

(sin²Ф + cos²Ф - 2sinФcosФ) + (sin²Ф + cos²Ф +2sinФcosФ)

We know that : sin²Ф + cos²Ф = 1

So,

( 1 - 2sinФcosФ) + (1 + 2sinФcosФ)

or 1 + 1 -2sinФcosФ + 2sinФcosФ

or 2

Hence we got  (sinФ - cosФ)² + (sinФ + cosФ)² = 2

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step-by-step explanation:

11.2

step-by-step explanation:

when doing tangent the tangent of the angle is equal to the opposite side from the angle over the adjacent side to the angle.

tan43 = x / 12

move 12 over by multiplying each side by 12

12tan43 = x

x = about 11.2