Question

If sin∅+cos∅=√2sin (90°-∅), determine cot∅.

Answer 1

SOLUTION

Consider,

=)sin∅+ cos∅= √2sin(90°-∅)

=)sin∅ + cos∅= √2 cos∅

=)sin∅= √2cos∅ - cos∅=(√2-1)cos∅

$= > \frac{sin \theta}{cos \theta} = \frac{( \sqrt{2} - 1)cos \theta}{cos \theta}$

=)tan∅= (√2-1)

=) cot∅= 1/(√2-1)

$= > cot \theta = \frac{( \sqrt{2 } + 1)}{( \sqrt{2} - 1)( \sqrt{2} + 1) } \\ = > \frac{( \sqrt{2} + 1}{2 - 1} \\ \\ = >cot \theta = \sqrt{2} + 1$

Hope it helps ☺️

Answer 2

Step-by-step explanation:

Check the attachment :)