If `tantheta+cottheta=5` then `tan^(2)theta+cot^(2)theta` is
A. 23
B. 24
C. 25
D. 26
A. 23
B. 24
C. 25
D. 26
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Correct Answer – a
Given
`tan theta+cot thea=5`
`rArrtantheta+cot theta=5`
`rArr[tan theta+cottheta]^(2)=5^(2)`
(squaring both sides)
`rArrtan^(2)theta+cot^(2)theta+2tan thetacottheta=25`
`rArrtan^(2)theta+cot^(2)theta=25-2[because tan theta . cot theta=1]`
` rArr tan^(2)theta+cot^(2)theta=23`