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Question
Taking θ = 30° to verify the following trigonometric identity:
1 + tan2θ = sec2θ
Theorem
Solution
Given: θ = 30°
To prove: 1 + tan2θ = sec2θ
Proof:
L.H.S. = 1 + tan2θ
= 1 + tan230°
= `1 + (1/sqrt3)^2`
= `1 + 1/3`
L.H.S. = `4/3` ...(i)
Now, R.H.S. = sec2θ
= sec230°
= `(2/sqrt3)^2`
R.H.S. = `4/3` ...(ii)
∴ L.H.S. = R.H.S. ...[From equations (i) and (ii)]
∴ 1 + tan2θ = sec2θ
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