Question

sec theta- tan theta equal to 4 .prove that cos theta equal to 8/17​

Answer 1

Answer:

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Step-by-step explanation:

Answer 2

Proving L.H.S =R.H.S

Step-by-step explanation:

$\ Given \ value:\\\\\sec \theta - \tan \theta = 4\\\\ \ prove \ that :\\\\\ cos \theta= \frac{8}{17} \\\\\ Solution:\\\\\sec \theta - \tan \theta = 4\\\\\rightarrow \sec \theta =4+ \tan \theta\\\\ \ Square \ the \ value:\\\\\rightarrow (\sec \theta)^2 =(4+ \tan \theta)^2\\\\\rightarrow \sec^2 \theta = 16+ \tan^2 \theta+ 8\tan \theta\\\\\rightarrow \sec^2 \theta -\tan^2 \theta= 16+ 8\tan \theta\\\\\rightarrow 1 = 16+ 8\tan \theta\\\\\rightarrow 16-1+ 8\tan \theta=0$

$\rightarrow 15+ 8\tan \theta= 0\\\\\rightarrow 8\tan \theta= -15\\\\\rightarrow \tan \theta=\frac{-15}{8}$

$\ base = 8\\\\\ hypotenuse = 17 \\\\\ perpendicular= -15 \\\\ \cos \theta = \frac{base}{hypotenuse}\\\\\cos \theta = \frac{8}{17}$

L.H.S= R.H.S

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• Proving: https://brainly.in/question/8112701