Question

If 5 tana = 4, then find the value of seca using suitable identity.​

Answer 1

5 tan a = 4

tan a = 4/5

Now,

1 + tan² a = sec² a

1 + ( 4 / 5 )² = sec² a

1 + 16 / 25 = sec² a

25 - 16 / 25 = sec² a

9 / 25 = sec² a

Therefore, sec a = 3 / 5

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Answer 2

5 tan a = 4

tan a = 4/5

Now,

1 + tan² a = sec² a

1 + ( 4 / 5 )² = sec² a

1 + 16 / 25 = sec² a

25 - 16 / 25 = sec² a

9 / 25 = sec² a

Therefore, sec a = 3 / 5