Q. 73.9( 15 Votes )
Prove that
(i) 
(ii) 
(iii) tan 150 + cot 150 = 4
Answer :
(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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