Question

If sec(7-2A)=cosec(5A-7), then find the value of A and hence evaluate sin3A+sec2A+cotA

Answer 1

sec(7-2A)=cosec(5A-7)
or, sec(7-2A)=sec{90°-(5A-7)}
or, 7-2A=90°-5A+7
or, -2A+5A=90°
or, 3A=90°
or, A=30°
∴, sin3A+sec2A+cotA
=sin(3×30°)+sec(2×30°)+cot30°
=sin90°+sec60°+cot30°
=1+2+√3
=3+√3
=√3(√3+1) Ans.