Question

cot^2 25.cosec^2 25(tan^2 25-sin^225)

Answer 1

Answer:

1

Step-by-step explanation:

cot^225*cosec^2 25 (tan^2 25-sin^2 25 )

= cot^2 25* cosec ^2 25 (1/cot ^2 25 -1/ csc ^2 25)

=cot ^2 25 *cosec ^2 25 (csc^2 25- cot ^2 25 )

=csc^2 25 -cot^2 25

=1

csc= cosec

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Answer 2

Given,

An expression: cot^2 25.cosec^2 25(tan^2 25-sin^2 25)

To find,

The value of the expression.

Solution,

We can simply solve this mathematical problem using the following process:

As per trigonometry,

If A is any angle, then,

tan A × cot A = 1

sin A × cosec A = 1

cosec^2 A - cot^2 A = 1

{Equation-1}

Now, according to the question;

The given expression

= cot^2 25.cosec^2 25(tan^2 25-sin^2 25)

On expanding the given expression, we get;

= cot^2 25.cosec^2 25.tan^2 25 - cot^2 25.cosec^2 25.sin^2 25

= cosec^2 25 × (cot^2 25.tan^2 25) - cot^2 25 × (cosec^2 25.sin^2 25)

= cosec^2 25 × (cot 25. tan 25)^2 - cot^2 25 × (cosec 25. sin 25)^2

= cosec^2 25 × (1)^2 - cot^2 25 × (1)^2

{according to equation-1}

= cosec^2 25 - cot^2 25

= 1

{according to equation-1}

Hence, the value of the given expression is equal to unity.