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Home » Choose the correct answer from the given four options: If cos A = 4/5, then the value of tan A is
Choose the correct answer from the given four options: If cos A = 4/5, then the value of tan A is
CBSE | Class 10 | Exercise 8.1 | Maths | NCERT Exemplar | Trigonometry and Its Equations
Choose the correct answer from the given four options: If cos A = 4/5, then the value of tan A is

(A) 3/5 (B) ¾ (C) 4/3 (D) 5/3

(B) 3/4

As indicated by the inquiry,

    \[cos\text{ }A\text{ }=\text{ }4/5\text{ }\ldots \text{ }\left( 1 \right)\]

We know,

    \[tan\text{ }A\text{ }=\text{ }sinA/cosA\]

To discover the worth of transgression A,

We have the condition,

    \[sin2\text{ }\theta \text{ }+cos2\text{ }\theta \text{ }=1\]

In this way,

    \[sin\text{ }\theta \text{ }=\text{ }\surd \text{ }\left( 1-cos2\text{ }\theta \right)\]

Then, at that point,

    \[\begin{array}{*{35}{l}} <!-- /wp:paragraph --> <!-- wp:paragraph --> ~ \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> sin\text{ }A\text{ }=\text{ }\surd \text{ }\left( 1-cos2\text{ }A \right)\text{ }\ldots \text{ }\left( 2 \right) \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> \end{array}\]

    \[sin2\text{ }A\text{ }=\text{ }1-cos2\text{ }A\]

    \[sin\text{ }A\text{ }=\text{ }\surd \left( 1-cos2\text{ }A \right)\]

Subbing condition (1) in (2),

We get,

    \[Sin\text{ }A\text{ }=\text{ }\surd \left( 1-\left( 4/5 \right)2 \right)\]

    \[=\text{ }\surd \left( 1-\left( 16/25 \right) \right)\]

= √(9/25)

= ¾

i

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