Question

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Prove that:
3. (sin a cos ß + cos a sin B)² + (cos a cos ß -sin o sin ß)² = 1.
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Answer 1

Answer:

1

Step-by-step explanation:

$(Sin A Cos B+ Cos A Sin B)^{2} + (Cos A Cos B - Sin A Sin B)^{2}$

=

$Sin^{2} A Cos^{2}B + Cos^{2} A Sin^{2} B + 2 Sin A Cos B Cos A Sin B + \\ Cos^{2} A Cos^{2} B + Sin^{2} A Sin^{2} B - 2 Sin A Sin B Cos A Cos B$

=

Sin^{2} A Cos^{2}B + Cos^{2} A Sin^{2} B + Cos^{2} A Cos^{2} B + Sin^{2} A Sin^{2} B

=

Sin^{2} A (Cos^{2}B + Sin^{2} B ) + Cos^{2} A (Sin^{2} B +Cos^{2} B )

=

Sin^{2} A (1) + Cos^{2} A (1)

= 1