Question

if cos theta = 12/ 13 , find the value of sin theta ( 1-tan theta )

Answer 1

35/156 is the answer

Answer 2

The value of $\sin \theta (1-\tan \theta)=\dfrac{35}{156}$.

Step-by-step explanation:

We have,

$\cos \theta=\dfrac{12}{13}$

To find, the value of $\sin \theta (1-\tan \theta)=?$

∴$\cos \theta=\dfrac{12}{13}=\dfrac{b}{h}$

∴ $p=\sqrt{h^{2}-b^{2}}$

Where, b =base, p = perpendicular and h = hypotaneous

$p=\sqrt{13^{2}-12^{2}}=\sqrt{165-144}$

$=\sqrt{25} =5$

∴ $\sin \theta=\dfrac{p}{h}=\dfrac{5}{13}$ and

$\tan \theta=\dfrac{p}{b}=\dfrac{5}{12}$

The value of $\sin \theta (1-\tan \theta)$

$=\dfrac{5}{13} (1-\dfrac{5}{12})$

$=\dfrac{5}{13} (\dfrac{12-5}{12})=\dfrac{5}{13} \times \dfrac{7}{12}$

$=\dfrac{35}{156}$

Thus, the value of $\sin \theta (1-\tan \theta)=\dfrac{35}{156}$.