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Grade: 12

                        

Question no. 15 in the given image please,with a brief explanation as well??

one year ago

Answers : (1)

Aditya Gupta
2065 Points
							
hello sridev there is a slight mistake in the ques. the modulus sign shouldnt be on the denominator. other than that the ques is right.
note that a×b + d×a + b×d= (b – a)×(d – a)= pq*sintheta, where p and q are respectively the magnitudes of (b – a) and (d – a).
so, the first term becomes pq*sintheta/(b – a).(d – a) but (b – a).(d – a)= pq*costheta.
so it becomes pq*sintheta/pq*costheta= tan(theta).
similarly, the second term shall become tan(phi). here, theta and phi are opposite angles. in a cyclic quad, we know that they add upto 180 deg. hence phi= 180 – theta.
so, first term is tan(theta).while second term is tan(80 – theta)= – tan(theta).
adding, we get zero.
kindly approve :=)
one year ago
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