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Some Applications Of Trigonometry

Question
CBSEENMA10007879
Wired Faculty App

If tanθ space equals space 4 over 3 comma what is the value of fraction numerator sinθ plus cosθ over denominator sinθ minus cosθ end fraction ?

Solution
Let us draw a right angle triangle, right angled at B.
We know that
tan squared straight theta space equals space 4 over 3 equals AB over AC
Let,AB -4K. BC -3K
Where K is positive number.
Using pythagoras theorem, we have
⇒ AC2 = AB2 + BC2
= (4K)2 + (3K)2
= 16K2 + 9K2
= 25 K2
So AC = 5K
Now, AB = 4K, BC =  3K and AC = 5K
Therefore,

fraction numerator sinθ plus cosθ over denominator sinθ minus cosθ end fraction space equals space fraction numerator begin display style AB over AC end style plus begin display style BC over AC end style over denominator begin display style AB over AC end style minus begin display style BC over AC end style end fraction
equals space fraction numerator begin display style fraction numerator 4 straight K over denominator 5 straight K end fraction end style plus begin display style fraction numerator 3 straight K over denominator 5 straight K end fraction end style over denominator begin display style fraction numerator 4 straight K over denominator 5 straight K end fraction end style minus begin display style fraction numerator 3 straight K over denominator 5 straight K end fraction end style end fraction space equals space fraction numerator begin display style 4 over 5 end style plus begin display style 3 over 5 end style over denominator begin display style 4 over 5 end style minus begin display style 3 over 5 end style end fraction space equals space fraction numerator begin display style fraction numerator 4 plus 3 over denominator 5 end fraction end style over denominator begin display style fraction numerator 4 minus 3 over denominator 5 end fraction end style end fraction space equals space fraction numerator 7 minus 4 over denominator 1 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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