show that equation cosec x= 4ab/(a+b)2 (ab 0) is possible if a=b - Maths - Trigonometric Functions

Question

show that equation cosec x= 4ab/(a+b)2 (ab>0) is
possible if a=b

ramandeep.singh · Accepted Answer

We know that numerically $c o \sec θ \geq 1$ .

$∴ {c o \sec}^{2} θ \geq 1 \Rightarrow \frac{4 a b}{(a + b)^{2}} \geq 1 \Rightarrow 4 a b \geq a^{2} + b^{2} + 2 a b \Rightarrow a^{2} + b^{2} - 2 a b \leq 0 \Rightarrow (a - b)^{2} \leq 0 ∴ (a - b)^{2} = 0 (∵ s q u a r e o f a n u m b e r c a n' t b e - v e) \Rightarrow a - b = 0 ∴ a = b$

∴The equation $\cos e c x = \frac{4 a b}{(a + b)^{2}}$ is possible only if a = b.

show that equation cosec x= 4ab/(a+b)2 (ab>0) is possible if a=b

show that equation cosec x= 4ab/(a+b)² (ab>0) is possible if a=b