Question

evaluate sin30+tan45-cosec60÷sec30+cos60+cot45

Answer 1

Answer:

(sin30+tan45-cosec60)/(sec30+cos60+cot45).

sin30=1/3.

tan45=1.

cosec60=2/√3.

sec30=2/√3.

cos60=1/2.

cot45=1.

(sin30+tan45-cosec60)/(sec30+cos60+cot45)=(1/2+1-2/√3)/(2/√3+1+1/2).

=(3/2-2/√3)/(3/2+2/√3). (Because 1/2+1=3/2).

=(3√3-4/2√3)/3√3+4/2√3). (Because LCM of 2 & √3 is 2√3).

=(3√3-4)/(3√3+4).

Rationalising denominator of 3√3+4 is 3√3-4.

Multiply numerator & denominator by 3√3-4.

=(3√3-4)/(3√3+4)×(3√3-4)/(3√3-4).

=(3√3-4)²/(3√3)²-(4)². (Because (a+b)×(a-b)=a²-b² where a=3√3 & b=4).

=(3√3)²+(4)²-2(3√3)(4)/9×3-16. (Because (a-b)²=a²+b²-2ab where a=3√3 & b=4).

=9×3+16-24√3/27-16.

=27+16-24√3/11.

=43-24√3/11.

I think this is your answer.