Question

given sec theta = 5/4 find tan theta/2

Answer 1

Hey !!!

sec¢ = 5/4

cos¢ = 4/5 [•°• 1/cos¢ = sec¢ ]

•°• tan¢/2 = sin¢/2 /cos¢/2

but , sin¢/2 = √1 -cos¢ /2

and cos¢/2 = √1 + cos¢ /2

dividing sin¢/2 /cos¢/2

we get ,

tan¢/2 = √ 1 - cos¢ /√ 1+ cos¢

=>√ 1 - cos¢ /1 + cos¢

=> √1 - 4/5
------------------
√1 + 4/5

=> √5 - 4 /5
-----------------
√9/5

=> 1/3

hence, tan¢/2 = 1/3 Answer ✔

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Hope it helps you !!!

@Rajukumar111