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What is the value of \(\frac{{cosec\;\left( {78^\circ - \theta } \right) - \sec \left( {12^\circ \; + \;\theta } \right) - \tan \left( {67^\circ \; + \;\theta } \right)\; + \;\cot \left( {23^\circ - \theta } \right)}}{{\tan 13^\circ \tan 37^\circ \tan 45^\circ \tan 53^\circ \tan 77^\circ }}?\)

What is the value of \(\frac{{cosec\;\left( {78^\circ - \theta } \right) - \sec \left( {12^\circ \; + \;\theta } \right) - \tan \left( {67^\circ \; + \;\theta } \right)\; + \;\cot \left( {23^\circ - \theta } \right)}}{{\tan 13^\circ \tan 37^\circ \tan 45^\circ \tan 53^\circ \tan 77^\circ }}?\) Correct Answer 0

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As we know,

cosec (90 – θ) = sec θ and tanθ cotθ = 1 and tan 45 = 1 and tan θ tan (90 – θ) = 1

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