Buktikan tan kuadrat (90derjat-x).sin kuadrat x + cotan kuadrat (90derjat-x).cos kuadrat x = 1.... Question from @ikrima27

ikrima27 @ikrima27

October 2018 2 72 Report

Buktikan tan kuadrat (90derjat-x).sin kuadrat x + cotan kuadrat (90derjat-x).cos kuadrat x = 1

xkuadratz (tan²(90°-x).sin²x) + (cot²(90°-x).cos²x) = 1
cos²x + sin²x = 1
1 = 1 (terbukti)

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ikrima27 terimakasih banyak

ImmanuelSinaga $$\begin{align}tan^2(90-x)\bullet sin^2x~+~cotan^2(90-x) \bullet cos^2x~~~&=~1 \\ \boxed{\bold{(tan~(90-x)~=~cotan~x)~dan~(cotan~(90-x)~=~tan~x)}}&\\ cotan^2x~\bullet~sin^2x~+~tan^2x \bullet cos^2x~~~&=~1 \\ \boxed{\bold{tan~x~=~\frac{sin~x}{cos~x}~~dan~~cotan~x~=~\frac{cos~x}{sin~x}}} \\ \left(\frac{cos^2x}{\not sin^2x}\right)\times \not sin^2x~+~\left(\frac{sin^2x}{\not cos^2x}\right) \times \not cos^2x~~~&=~1 \\ cos^2x~+~sin^2x~~~&=~1 \\ 1~~&=~~1 \\ \\ \boxed{terbukti}&\end{align}$

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