Question

Without using trigonometric tables evaluate- cot 30/sec30+cosec30/tan45 - 2cos0/sin30 +cos power2 45

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

The value of the given trigonometric expression is 0.

Explanation:

Here , we  need to evaluate the trigonometric expression :  $\dfrac{\cot 30^{\circ}}{\sec30^{\circ}}+\dfrac{\text{cosec}30^{\circ}}{\tan45^{\circ}}-\dfrac{2\cos0^{\circ}}{\sin30^{\circ}}+\cos^245^{\circ}$

By using the trigonometric table , we have

$\because \cot 30^{\circ}=\sqrt{3}\ ,\ \sec30^{\circ}=\dfrac{2}{\sqrt{3}}\ , \text{cosec}30^{\circ}=2\\\\\tan45^{\circ}=1\ ,\ \cos0^{\circ}=1\ ,\ \cos45^{\circ}=\dfrac{1}{\sqrt{2}}$

$\\\\\therefore \dfrac{\cot 30^{\circ}}{\sec30^{\circ}}+\dfrac{\text{cosec}30^{\circ}}{\tan45^{\circ}}-\dfrac{2\cos0^{\circ}}{\sin30^{\circ}}+\cos^245^{\circ}\\\\=\dfrac{\sqrt{3}}{\dfrac{2}{\sqrt{3}}}+\dfrac{2}{1}-\dfrac{2}{\dfrac{1}{2}}+(\dfrac{1}{\sqrt{2}})^2\\\\=\dfrac{(\sqrt{3})^2}{2}+2-(2)^2+\dfrac{1}{2}\\\\\\=\dfrac{3}{2}+2-4+\dfrac{1}{2}=0$

Therefore , the value of the given trigonometric expression is 0.

# Learn more :

Tan45°/cosec30°+sec60°/cot45°-5sin90°/2cos0°​

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