Home
Class 9
MATHS
Prove ( 1 - sin 60^@)/ ( cos 60^@) = ( ...

Prove ` ( 1 - sin 60^@)/ ( cos 60^@) = ( 1 - tan 30^@)/ ( 1+ tan 30^@)`

Text Solution

Verified by Experts

`L.H.S. = (1-sin60^@)/cos60^@`
`=(1-sqrt3/2)/(1/2) = 2-sqrt3`
`R.H.S. = (1-tan30^@)/(1+tan30^@)`
`=(sqrt3-1)/(sqrt3+1)**(sqrt3-1)/(sqrt(3-1)`
`=(4-2sqrt3)/2 = 2-sqrt3`
`:. L.H.S. = R.H.S.`
Promotional Banner

Similar Questions

Explore conceptually related problems

Prove that: cos 60=(1-(tan 30)^2)/(1+(tan 30)^2)

Verify:a. Sin60^@=(2tan30^@)/(1+tan^2 30^@)

(2tan3 0^(@))/(1-tan^2 3 0^(@)) is equal to (a) sin60^(@) (b) cos60^(@) (c) tan60^(@) (d) sin30^(@)

(tan 60^(@) - tan 30^(@))/(1 + tan 60^(@) tan 30^(@)) equal

Verify that cos 60^(@)=(1-tan^(2)30^(@))/(1+tan^(2)30^(@))

The value of (sin 30^@ sin 60^@)/(cos 60^@ cos 30^@)-tan45^@ is : (sin 30^@ sin 60^@)/(cos 60^@ cos 30^@)-tan45^@ का मान है?

Find (in each case, given below) the value of x, if : tan x = (tan 60^(@) - tan 30^(@))/(1 + tan 60^(@) tan 30^(@))

Show that : (i) (1-sin60^(@))/(cos60^(@))=(tan60^(@)-1)/(tan60^(@)+1) (ii) (cos30^(@)+sin60^(@))/(1+sin30^(@)+cos60^(@))=cos30^(@)

Verify that sin60^(@)=(2tan 30^(@))/(1+tan^(2)30^(@))

If x tan 30^(@) = (sin 30^(@) + cos 60^(@))/( tan 60^(@) + sin 60^(@)) , then the value of x is :