Question

If cos thetha =1/2 then find the value of 2 Sec thetha/1+tan² thetha​


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Answer 1

★GIVEN:-

cos ø=1/2

★TO FIND OUT

2secØ/(1+tan²Ø)

★SOLUTION:-

We know that cos ø= 1/2 =base / Hypotenuse

Thus let base = 1x and Hypotenuse =2x

By pythagorus theorum,

Hypotenuse²= perpendicular ²+base ²or H²=P²+B²

P²=H²-B²

P²= (2x)²-(x)²

P= ✓3x

Now ,

Sec ø= Hypotenuse/base = 2

tan² ø=perpendicular/base = (✓3)²=3

Now we have ⇒2sec ø/(1+tan²ø) ⇒2×2/1+3⇒4/4⇒1

Another method

we have

cos ø=1/2

And we also know that

cos 60⁰= 1/2

cos ø= cos 60⁰

ø=60⁰

Thus , Putting the value of ø in given expression

⇒2 sec 60⁰/ 1+ tan² 60⁰

⇒2×2/1+(✓3)²

⇒4/4

⇒1

Answer 2

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