Question

Tan 45 ÷ sin 30 + cos 30 = root 3 - 1

Answer 1

Step-by-step explanation:

Ans.  = (4 + root3) / 2

tan 45/sin 30 + cos 30

= 1/(1/2) + root3/2

=2/1 + root3/2

= LCM

=2/(4 + root3)

Answer 2

Proof:

We know that,

tan45° = 1

sin30° = 1/2

cos30° = √3 / 2

∴ L.H.S. = tan45° ÷ (sin30° + cos30°)

= 1 ÷ (1/2 + √3 / 2)

= 1 ÷ {(1 + √3)/2}

= 1 / {(1 + √3)/2}

= 2 / (√3 + 1)

= 2 (√3 - 1) / {(√3 + 1) (√3 - 1)}

= 2 (√3 - 1) / (3 - 1)

= 2 (√3 - 1) / 2

= √3 - 1 = R.H.S.

Hence, proved.