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Introduction of Trigonometry and its Application — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsIntroduction of Trigonometry and its Application1 Mark
MCQ
Choose the correct answer from the given four options.
The value of the expression $[\text{cosec}(75^\circ+\theta)-\sec(15^\circ-\theta)-\tan(55^\circ+\theta)+\cot(35^\circ-\theta)]$ is:
  • A
    –1
  • ✓
    0
  • C
    1
  • D
    $\frac{3}{2}$
✓

Answer

Correct option: B.
0
Given, expression $=\text{cosec}(75^\circ+\theta)-\sec(15^\circ-\theta)-\tan(55^\circ+\theta)+\cot(35^\circ-\theta)$$=\text{cosec}[90^\circ-(15^\circ-\theta)]-\sec(15^\circ-\theta)-\tan(55^\circ+\theta)+\cot(90^\circ-(55^\circ+\theta))$
$=\sec(15^\circ-\theta)-\sec(15^\circ-\theta)-\tan(55^\circ+\theta)+\tan(55^\circ+\theta)$
$[\therefore\text{cosec}(90^\circ-\theta)=\sec\theta\text{ and }\cot(90^\circ-\theta)=\tan\theta]$
$=0$
Hence, the required value of the given expression is 0.

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