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Find the value of A. A+{}^{2}A-cosec A, if A=2

Question

Find the value of
$sec A . tan A + tan^{2} A - cosec A$ , if $tan A = 2$

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Daniel Discussed

Find the value of

sec A . tan A + tan^{2} A - cosec A

, if

tan A = 2

8 mins ago

Discuss this question LIVE

8 mins ago

Text solutionVerified

Given:

tan A = 2 \Rightarrow tan^{2} A = 4

we know that

sec^{2} A = 1 + tan^{2} A \Rightarrow sec^{2} A = 1 + 4 \Rightarrow sec^{2} A == 5 \Rightarrow sec A = 5 \Rightarrow cos A = \frac{1}{5}

now we know that

tan A = \frac{sin A}{cos A}

\Rightarrow 2 = \frac{sin A}{\frac{1}{5}} \Rightarrow 2 = 5 sin A \Rightarrow sin A = \frac{2}{5} \Rightarrow co sec A = \frac{5}{2}

now putting all the values in the given equation
we get

\Rightarrow (5) (2) + (4) - (\frac{5}{2}) = \frac{3 5 + 8}{2}

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Question Text	Find the value of $sec A . tan A + tan^{2} A - cosec A$ , if $tan A = 2$
Answer Type	Text solution:1
Upvotes	150