Question

cosec2 30 sin2 45-sec2 60

Answer 1

Correct Question:

Evaluate :

Cosec2 30° - sin2 45° -sec2 60°

Solution :

We know that

Cosec 30° = 2, sin45° = 1/√2 and sec60° =  2

therefore  cosec2 30 × sin2 45° - sec2 60° = 2×2 -1/2-4 = -1/2

hence cosec2 30°- sin2 45° - sec2 60° =  -1/2

Answer 2

Answer:

-2

Step-by-step explanation:

cosec2 30 sin2 45-sec2 60

$Cosec^230 Sin^245 - Sec^260\\\\Cosec = \frac{1}{Sin} \:\&\: Sec =\frac{1}{Cos} \\\\=\frac{1}{Sin^230} \times Sin^245 - \frac{1}{Cos^260} \\\\Cos\theta = Sin(90-\theta) \implies Cos60 = Sin30\\\\ = \frac{1}{Sin^230} \times Sin^245 - \frac{1}{Sin^230}\\\\= \frac{1}{Sin^230} \times (Sin^245 - 1)\\\\Sin30 = \frac{1}{2}\:\: \& \:Sin45 = \frac{1}{\sqrt{2}} \\\\= \frac{1}{(\frac{1}{2})^2} \times((\frac{1}{\sqrt{2}})^2 - 1 )\\\\= 4 \times (\frac{1}{2} -1)\\\\= 4\times(-\frac{1}{2} )\\\\= -2$