jawaban identitas trigonometri (secan B - cosec B) (sin B + cos B) = tan B x cotan B

Bab Trigonometri
Matematika SMA Kelas X

(secan B - cosec B) (sin B + cos B) 
= secan B . sin B + secan B . cos B - cosec B . sin B - cosec B . cos B
= (1/cos B) . sin B + (1/cos B) . cos B - (1/sin B) . sin B - (1/sin B) . cos B
= tan B + 1 - 1 - cotan B
= tan B - cotan B

Verifying Trigonometry Identity.

[tex]\displaystyle (\sec B-\csc B)(\sin B+\cos B)\\ =\left ( \frac{1}{\cos B}-\frac{1}{\sin B} \right )(\sin B+\cos B)\\ =\frac{(\sin B-\cos B)(\sin B+\cos B)}{\cos B \sin B}\\ =\frac{\sin^2 B-\cos^2 B}{\cos B \sin B}\\ =\frac{\sin B}{\cos B}-\frac{\cos B}{\sin B}\\ =\tan B-\cot B[/tex]

Not proved.