2tan-1(1/5) + sec-1 (5* 21/2/7) + 2tan-1(1/8) - Maths - Integrals

Question

2tan-1(1/5) + sec-1 (5* 21/2/7) +
2tan-1(1/8)

Rajat Sethi · Accepted Answer

y=2tan-118+2tan-115+sec-1527Now,sec-1527=cos-1752=π2-sin-1752Now, as shown,A triangle with hypotenuse as  hypotenuse  52 and one side 7 will have the last side of unit 1
So,sin-1752=tan-17thus,sec-1527=π2-tan-17y=2tan-118+2tan-115+π2-tan-17y=π2+2(tan-118+151-18×15)-tan-17y=π2+2tan-113-tan-17y=π2+tan-1231-(13)2-tan-17y=π2+tan-134-tan-17y=π2+tan-134-71+34×7y=π2+tan-1(-1)y=π2-π4=π4<img alt=""
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