Question

If cos cos theta = 1, the value of sin ²theta + Sin ²theta is
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Answer 1

Step-by-step explanation:

Let the breadth of the rectangle be x cm.

Then, the length of the rectangle is (x+9) cm.

So, area of rectangle = length x breadth =x(x+9)cm

2

Now, length of new rectangle =(x+9+3) cm =(x+12) cm and

breadth of new rectangle =(x+3) cm.

So, area of new rectangle = length × breadth =(x+12)(x+3)cm

2

According to the given condition,

(x+12)(x+3)=x(x+9)+84

⇒x

2

+12x+3x+36=x

2

+9x+84

⇒15x+36=9x+84

⇒15x−9x=84−36

⇒6x=48

⇒x=8

So, breadth of the rectangle is 8 cm and length

=8+9=17 cm.

Answer 2

Cos2theta value is

I.e, cox2x=cos(x+x)

The formula for cos(a+b) is cosa.cosb-sina.sinb

Here ,a=x & , b=x

Then , put the value,s of a&b

We have

Cos2x= cosx.cosx- sinx.sinx.

Cos2x= cos²x- sin²x .

Here we know that sin²x = 1- cos²x then put

Cos2x = cos²x- ( 1- cos²x) we have ,

= cos²x- 1+ cos²x

Cos2x= 2cos²x- 1 this is an other value for Cos double angle.

Cos2x+1=2cos²x it is also value for cos

±underroot cos2x+1/2 = cos²x

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