Trigonometry problem

Geometry Level 1

Given that sec ⁡ B + tan ⁡ B = 5 2 \sec B + \tan B = \dfrac 52 . Find sec ⁡ B − tan ⁡ B \sec B - \tan B .


The answer is 0.4.

Munem Shahriar by Munem Shahriar , 18, Bangladesh

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1 solution

Munem Shahriar
Jan 25, 2018

We know that,

sec ⁡ 2 B = 1 + tan ⁡ 2 B sec ⁡ 2 B − tan ⁡ 2 B = 1 ( sec ⁡ B + tan ⁡ B ) ( sec ⁡ B − tan ⁡ B ) = 1 5 2 ( sec ⁡ B − tan ⁡ B ) = 1 sec ⁡ B − tan ⁡ B = 2 5 = 0.4 \begin{aligned} \sec^2 B &= 1 + \tan^2 B \\\sec^2 B - \tan^2 B &=1\\(\sec B + \tan B)(\sec B - \tan B) &=1 \\\dfrac 52(\sec B - \tan B) & = 1\\\sec B - \tan B & = \dfrac 25 = \boxed{0.4} \\ \end{aligned}

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