# Prove that(i) (ii) (iii) tan 150 + cot 150 = 4

(i)sin75° = sin(90° - 15°) .…….(using sin(A - B) = sinAcosB - cosAsinB)

= sin90°cos15° - cos90°sin15°

= 1.cos15° - 0.sin15°

= cos15°

Cos15° = cos(45° - 30°) …………(using cos(A - B) = cosAcosB + sinAsinB)

= cos45°.cos30° + sin45°.sin30°

(ii)(using sin(180° - x) = sinx)

(using cos(180° - x) = - cosx)

=

(iii)tan15° + cot15° =

First, we will calculate tan15°,

………………….(1)

Putting in eq(1),

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