If sec- -tan- -ab- then the value of tan- is

The correct option is C b^2 a^22ab We #10;have, #10; #10; #10;θ tanθ =ab #10; #10; #160; #10; #10;We #10;know that #10; #10; ...

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Standard X

Mathematics

Standard Values of Trigonometric Ratios

If secθ -ta...

Question

If $s e c θ - t a n θ = \frac{a}{b},$ then the value of $t a n θ$ is

\frac{a - b}{2 a b}

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\frac{a^{2} - b^{2}}{2 a b}

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\frac{b^{2} - a^{2}}{2 a b}

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\frac{b - a}{2 a b}

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Solution

The correct option is C $\frac{b^{2} - a^{2}}{2 a b}$
We have,

$sec θ - tan θ = \frac{a}{b}$

We know that

$sec θ = \sqrt{1 + {tan}^{2} θ}$

Therefore,

$\sqrt{1 + {tan}^{2} θ} - tan θ = \frac{a}{b}$

$\sqrt{1 + {tan}^{2} θ} = \frac{a}{b} + tan θ$

$1 + {tan}^{2} θ = \frac{a^{2}}{b^{2}} + {tan}^{2} θ + \frac{2 a}{b} tan θ$

$1 = \frac{a^{2}}{b^{2}} + \frac{2 a}{b} tan θ$

$\frac{2 a}{b} tan θ = \frac{b^{2} - a^{2}}{b^{2}}$

$tan θ = \frac{b^{2} - a^{2}}{2 a b}$

Hence, this is the answer.

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Q. More than One Answer Type
एक से अधिक उत्तर प्रकार के प्रश्न

If a – b = a² + b² + 2ab and a + b = a² + b² – 2ab, then which of the following is/are correct?

यदि a – b = a² + b² + 2ab तथा a + b = a² + b² – 2ab, तब निम्नलिखित में से कौनसा/कौनसे विकल्प सही है/हैं?

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If secθ−tanθ=ab, then the value of tanθ is

The correct option is C b2−a22abWe have, secθ−tanθ=ab We know that secθ=√1+tan2θ Therefore, √1+tan2θ−tanθ=ab √1+tan2θ=ab+tanθ 1+tan2θ=a2b2+tan2θ+2abtanθ 1=a2b2+2abtanθ 2abtanθ=b2−a2b2 tanθ=b2−a22ab Hence, this is the answer.

If $s e c θ - t a n θ = \frac{a}{b},$ then the value of $t a n θ$ is