If sin (3α - 45°) = cos (45° - 2α) then the value of  sinα + cos\(\frac{a}{2}\) + tan\(\frac{2a}{3}\) .

\(\frac{√2 + 1 + √6 }{\sqrt {2}}\)

[Concept: sin A = cos B, when A + B = 90°]

Therefore,

(3a - 45° + 45° - 2α) = 90°

α = 90°

Put this value in find →

⇒ sinα + cos \(\frac{a}{2}\) + tan \(\frac{2a}{3}\) 

⇒ sin90° + cos45° + tan60°

=  1 + \(\frac{1}{\sqrt {2}}\) + \(\sqrt { 3}\)

= \(\frac{√2 + 1 + √6 }{\sqrt {2}}\)