If x=cos−1(23)+tan−1(17) then x=
We have,
cos−123+tan−117
We know that,
tan−1x=cos−1(1√1+x2)
Therefore,
=cos−123+cos−1⎛⎜ ⎜ ⎜ ⎜ ⎜ ⎜⎝1√1+(17)2⎞⎟ ⎟ ⎟ ⎟ ⎟ ⎟⎠
=cos−123+cos−1(7√50)
We know that,
cos−1x+cos−1y=cos−1{xy−√1−x2√1−y2}
Therefore,
=cos−1⎧⎪⎨⎪⎩23×7√50−√1−(23)2 ⎷1−(7√50)2⎫⎪⎬⎪⎭
=cos−1{143√50−√59√150}
=cos−1{143√50−√53√50}
=cos−1{14−√53√50}
Hence, this is the answer.