Question

Evaluvate:1-cot2 45°/1+sin2 90°​

Answer 1

Answer:

0

Step-by-step explanation:

put the values of Cot 45 and Sin 90

you will get

Cot 45 = 1 and Sin 90 = 1

= 1 - 2(1)/1 + 2(1)

= 1 - 2 / 1 + 2

= -1/3

Answer 2

The question is

Evaluate: $\frac{1 - { \ \cot}^{2} {45}^{0} }{1 + { \sin }^{2} {90}^{0} }$

On evaluating the above expression we get 0.

Here, we have to evaluate the given trigonometric expression.

• Trigonometric ratios are the relation between the sides and angles of a right-angled triangle.
• Sine (Sin) is the ratio of the perpendicular to that of the hypotenuse and cotangent (cot) is the ratio of the base that of the perpendicular.

$\frac{1 - { \ \cot}^{2} {45}^{0} }{1 + { \sin }^{2} {90}^{0} }$

$= \frac{1 - { (\cot{45}^{0}) }^{2} }{1 + { (\sin{90}^{0}) }^{2} }$...........................(1)

We know that,

$\sin( {90}^{0} ) = 1$

$\cot( {45}^{0} ) = 1$

On putting the value of sin 90° and cot 45° in the above equation 1 we get,

$\frac{1 - {(1)}^{2} }{1 + {(1)}^{2} }= \frac{1 - 1}{1 + 1} =\frac{0}{2} = 0$

Hence, on evaluating $\frac{1 - { \ \cot}^{2} {45}^{0} }{1 + { \sin }^{2} {90}^{0} }$ we get 0.

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