Question

tan 45° + tan 30°/1-tan 45° * tan 30°​

Answer 1

Answer:

The answer is 2+√3

Step-by-step explanation:

(tan45°+tan30°)/(1-tan45°tan30°)

= (1+1/√3) / (1-1×1/√3)         [∵tan45°=1, tan30°=1/√3]

= (√3+1) / (√3-1)

= (√3+1)(√3+1) / (√3-1)(√3+1)

= (√3+1)² / {(√3)²-1²}

= {(√3)²+2√3+1} / (3-1)

= (3+2√3+1) / 2

= (4+2√3) / 2

= 2(2+√3) / 2

= 2+√3

Answer 2

Answer:

The Correct Answer is 2+√3

Step-by-step explanation:

(tan45°+tan30°)/(1-tan45°tan30°)

= (1+1/√3) / (1-1×1/√3)         [∵tan45°=1, tan30°=1/√3]

= (√3+1) / (√3-1)

= (√3+1)(√3+1) / (√3-1)(√3+1)

= (√3+1)² / {(√3)²-1²}

= {(√3)²+2√3+1} / (3-1)

= (3+2√3+1) / 2

= (4+2√3) / 2

= 2(2+√3) / 2

= 2+√3

Hope this help :)