Prove that: sin(45° +A) + cos(45° +A) =√2 cosA | Trigonometric Ratios of Compound Angles

Prove that: sin(45° +A) + cos(45° +A) =√2 cosA | Trigonometric Ratios of Compound Angles | Sci-Pi

Prove that:

Sin(45°+A) + cos(45°+A) =√2 cosA

Answer:

You need to understand the given formulas to be able to solve such types of Trigonometric values of compound angles questions and answers.

Solution:

Taking LHS

= sin(45°+A) +cos(45°+A)

= sin45°.cosA +cos45°.sinA + cos45°.cosA -sin45°.sinA

$\frac{1}{√2}$ .cosA +

$\frac{1}{√2}$ .sinA +

$\frac{1}{√2}$ .cosA -

$\frac{1}{√2}$ .sinA

$\frac{1}{√2}$ .cosA +

$\frac{1}{√2}$ .cosA

$\frac{cosA +cosA}{√2}$

$\frac{2cosA}{√2}$

= √2 cosA

= RHS

#proved

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Prove that: sin(45° +A) + cos(45° +A) =√2 cosA | Trigonometric Ratios of Compound Angles | Sci-Pi