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(cot54º/tan36º)+(tan20º/cot70º)−2 - Mathematics

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Sum

`(\text{i})\text{ }\frac{\cot 54^\text{o}}{\tan36^\text{o}}+\frac{\tan 20^\text{o}}{\cot 70^\text{o}}-2`

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Solution

We have,

`\frac{\cot 54^\text{o}}{\tan 36^\text{o}}+\frac{\tan20^\text{o}}{\cot70^\text{o}}-2`

`=\frac{\cot (90^\text{o}-36^\text{o})}{\tan36^\text{o}}+\frac{\tan 20^\text{o}}{\cot(90^\text{o}-20^\text{o})}-2`

`=\frac{\tan 36^\text{o}}{\tan36^\text{o}}+\frac{\tan 20^\text{o}}{\tan20^\text{o}}-2`

= 1 + 1 – 2 = 0

Concept: Trigonometric Ratios of Complementary Angles
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