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vodka [1.7K]
3 years ago
10

To prove :One plus cot square theta into tan theta by sec square theta = cot theta

Mathematics
1 answer:
pickupchik [31]3 years ago
6 0

we are given

\frac{(1+cot^2(\theta))*tan(\theta)}{sec^2(\theta)} =cot(\theta)

We will simplify left side and make it equal to right side

Left side:

\frac{(1+cot^2(\theta))*tan(\theta)}{sec^2(\theta)}

we can use trigonometric identity

1+cot^2(\theta)=csc^2(\theta)

we can replace it

\frac{(csc^2(\theta))*tan(\theta)}{sec^2(\theta)}

we know that

csc=1/sin and sec=1/cos

so, we can replace it

and we get

\frac{cos^2(\theta)tan(\theta)}{sin^2(\theta)}

now, we know that

tan =sin/cos

\frac{cos^2(\theta)*sin(\theta)}{sin^2(\theta)*cos(\theta)}

we can simplify it

and we get

\frac{cos(\theta)}{sin(\theta)}

we can also write it as

=cot(\theta)

Right Side:

cot(\theta)

we can see that

left side = right side

so,

\frac{(1+cot^2(\theta))*tan(\theta)}{sec^2(\theta)} =cot(\theta)......Answer

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