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Some Applications Of Trigonometry

Question
CBSEENMA10007608
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If sinA space equals space 3 over 4 comma space calculate cos A and tan A.

Solution
Let us draw a right angle triangle, right angled at B.
We know that:
space sin space straight A space equals space 3 over 4 space equals space BC over AC
 Let BC = 3K,  AC = 4K
where K is a positive number.

Using Pythagoras theorem, we have
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rightwards double arrow        space space space space space space left parenthesis 4 straight K right parenthesis squared space equals space AB squared plus left parenthesis 3 straight K right parenthesis squared
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rightwards double arrow              space AB squared space equals space 16 straight K squared minus 9 straight K squared
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Now,  cosA space equals space AB over AC equals fraction numerator square root of 7 straight K over denominator 4 straight K end fraction space equals fraction numerator square root of 7 over denominator 4 end fraction
and    tanA space equals space BC over AB equals fraction numerator 3 straight K over denominator square root of 7 straight K end fraction equals fraction numerator 3 over denominator square root of 7 end fraction.

Some More Questions From Some Applications of Trigonometry Chapter

Choose the correct option and justify your choice:
sin 2A = 2 sin A is true when A = 
(A) 0°         (B) 30°         (C) 45°       (D) 60°

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