Question

mathematics
class X
trigonometry
please hurry up
it's urgent ​

Answer 1

EXPLANATION.

• GIVEN

5) = m = cosecø + cotø

n = cosecø - cotø

PROVE THAT MN = 1.

put the value of m and n

( cosecø + cotø) ( cosecø - cotø)

it is in form of (a + b ) ( a - b) = a^2 - b^2

( cosec^2ø - cot^2ø ) = 1

Hence,proved

6) = m = secø + tanø

n = secø - tanø

PROVE THAT MN = 1.

put the value of m and n

( secø + tanø) ( secø - tanø)

it is in form of ( a - b) ( a + b) = a^2 - b^2

( sec^2ø - tan^2ø ) = 1

Hence,proved

Answer 2

Step-by-step explanation:

Since we know that,

1 + cot² theta = cosec² theta

=> cosec² theta - cot² theta = 1

and,

1 + tan² theta = sec² theta

=> sec² theta - tan² theta = 1

Now,

For Question 5.

we have,

m = (cosec theta + cot theta)

and n = (cosec theta - cot theta)

So,

mn = (cosec theta + cot theta)

*(cosec theta - cot theta)

= (cosec² theta - cot² theta)

= 1 proved....

Now,

For Question 6.

we have,

m = (sec theta + tan theta)

and n = ( sec theta - tan theta)

So,

mn = (sec² theta - tan² theta)

= 1 proved....