Question

if tan theta + sin theta equals to M and Express 4 tan theta sin theta in terms of m and n
please answer fast​

Answer 1

Answer:

Let a be the first term and d be the common difference of the given A.P. Then,

Sm​=n

⟹2m​{2a+(m−1)d}=n

⟹2am+m(m−1)d=2n               ...(i)

and, Sn​=m

⟹2n​{2a+(n−1)d}

⟹2an+n(n−1)d=2m          ...(ii)

Subtracting equation (ii) from equation (i), we get

2a(m−n)+{m(m−1)−n(n−1)}d=2n−2m

⟹2a(m−n)+{(m2−n2)−(m−n)}d=−2(m−n)

⟹2a+(m+n−1)d=−2          [On dividing both sides by (m−n)]        ...(iii)

Now,  

Sm+n​=2m+n​{2a+(m+n−1)d}

⟹Sm+n​=2m+n​(−2)          [Using (iii)]

⟹Sm+n​=−(m+n)

Step-by-step explanation: