Question

If Sec theta Tan theta =4 find sin theta , cos theta 

Answer 1

HEY!!

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▶sec A + tan A = 4

▶We know that, sec2 A - tan2 A = 1

▶(sec A + tan A)(sec A - tan A) = 1

▶sec A - tan A = 1/4

Now,

▶(sec A + tan A) + (sec A - tan A) = 4 + 1/4 = 17/4

▶2 sec A = 17/4

▶sec A = 17/8

▶cos A = 8/17

▶▶sin A = root [1 - 64/289] = root [225/289] = 15/17

Hence,

✔✔Sin A = 15/17 and cos A = 8/17

Answer 2

Hey

Here is your answer,

SecØ +TanØ=4
SecØ= 4-TanØ
squaring both sides
Sec²Ø= 16 + Tan²Ø- 8 TanØ
1+Tan²Ø=16 + Tan²Ø- 8 TanØ
we get 8Tan Ø= 15
TanØ=15/8
Tan²Ø= 225/64
Sec²Ø= 1+Tan²Ø
Sec²Ø= 289/64
SecØ =17/8
So CosØ=8/17
Sin²Ø=1-Cos²Ø = 1-64/289
Sin²Ø= 225/289
SinØ= 15/17

Cos Ø= 8/17 and Sin Ø= 15/17

Hope it helps you!