Question

If tan 0 = 5, where is an acute angle, find sec 0 using the identity.
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Answer 1

$\underline{ \sf \: Qᴜᴇsᴛɪᴏɴ -}$

If tan theta = 5, where theta is an acute angle, find sec theta using the identity.

$\underline{ \sf \: Sᴏʟᴜᴛɪᴏɴ -}$

$\sf \: 1 + { \tan }^{2} \theta \: = \: {sec}^{2} \theta \\ \sf \implies 1 + {5}^{2} \theta \: = \: {sec}^{2} \theta \\ \sf \implies \: 1 + 25 = {sec}^{2} \theta \\ \sf \implies \: {sec}^{2} \theta \: = \: 26 \\ \sf \implies \: sec \theta \: = \sqrt{26} ...$