Some Applications of Trigonometry

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Prove the following identity: - Wired Faculty

Question

Prove the following identity:
$left parenthesis secθ minus cosecθ right parenthesis space left parenthesis 1 plus tanθ plus cotθ right parenthesis space equals space secθ. space tanθ space minus space cosecθ. space cotθ$

Solution

straight L. straight H. straight S. space equals space left parenthesis secθ minus cosecθ right parenthesis space left parenthesis 1 plus tanθ plus space cotθ right parenthesis equals space open parentheses 1 over cosθ minus 1 over sinθ close parentheses space open parentheses 1 plus sinθ over cosθ plus cosθ over sinθ close parentheses equals space open parentheses fraction numerator sinθ minus cosθ over denominator cosθ. space sinθ end fraction close parentheses space open parentheses fraction numerator sinθ. space cosθ space plus sin squared straight theta plus cos squared straight theta over denominator cosθ. space sinθ end fraction close parentheses equals space fraction numerator sin cubed straight theta minus cos cubed straight theta over denominator sin squared straight theta. space cos squared straight theta end fraction equals space fraction numerator sin cubed straight theta over denominator sin squared straight theta. space cos squared straight theta end fraction minus fraction numerator cos cubed straight theta over denominator sin squared straight theta. space cos squared straight theta end fraction equals space fraction numerator sin space straight theta over denominator cos squared straight theta end fraction minus fraction numerator cosθ over denominator sin squared straight theta end fraction equals space fraction numerator sin space straight theta over denominator cos space straight theta end fraction cross times fraction numerator 1 over denominator cos space straight theta end fraction minus fraction numerator cos space straight theta over denominator sin space straight theta end fraction cross times fraction numerator 1 over denominator sin space straight theta end fraction equals space tanθ. space secθ space minus space cot space straight theta. space cosec space straight theta equals space straight R. straight H. straight S.

Hence, L.H.S. = R.H.S.

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Some Applications Of Trigonometry

Prove the following identity:
$left parenthesis secθ minus cosecθ right parenthesis space left parenthesis 1 plus tanθ plus cotθ right parenthesis space equals space secθ. space tanθ space minus space cosecθ. space cotθ$

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°

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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Email Address

Loaction

For Daily Free Study Material Join wiredfaculty

Some Applications Of Trigonometry

Prove the following identity:

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°

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Prove the following identity:
$left parenthesis secθ minus cosecθ right parenthesis space left parenthesis 1 plus tanθ plus cotθ right parenthesis space equals space secθ. space tanθ space minus space cosecθ. space cotθ$

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°