Question

(cot 30/sin 45)+((1-sin 45)/cot 30)

Answer 1

Step-by-step explanation:

(cot 30/sin 45)+((1-sin 45)/cot 30)

hey buddy

it is simple trigo angles so we can directly put values of angles

(√3 /1/√2) + (1-1/√2)/√3

√6 +1- √3/√2

Answer 2

$\frac{\cot 30}{\sin 45}+\frac{1-\sin 45}{\cot 30}=\frac{5+\sqrt2}{\sqrt6}$

Step-by-step explanation:

Given : Expression $\frac{\sec^2 60-\tan^2 60}{\sin^2 30+\cos^2 30}$

To find : Solve the expression ?

Solution :

Expression $\frac{\cot 30}{\sin 45}+\frac{1-\sin 45}{\cot 30}$

Using trigonometric values,

$\sin 45=\frac{1}{\sqrt2}$

$\cot 30=\sqrt3$

Substitute the values,

$=\frac{\sqrt 3}{\frac{1}{\sqrt2}}+\frac{1-\frac{1}{\sqrt2}}{\sqrt 3}$

$=\sqrt 3\times \sqrt2+\frac{\frac{\sqrt2-1}{\sqrt2}}{\sqrt 3}$

$=\sqrt 6+\frac{\sqrt2-1}{\sqrt6}$

$=\frac{6+\sqrt2-1}{\sqrt6}$

$=\frac{5+\sqrt2}{\sqrt6}$

Therefore, $\frac{\cot 30}{\sin 45}+\frac{1-\sin 45}{\cot 30}=\frac{5+\sqrt2}{\sqrt6}$

#Learn more

Tan(45+A)×tan(45-A)​

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