This is the basic and conceptual question from trigonometric ratios in which we have been asked to calculate the value of

(sin^2 30° + 4cot^2 45° – sec^2 60)(cosec^2 45° sec^2 30°)

RS Aggarwal, Class 10, chapter 11, question no 8

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## sin30∘=1/2

## ⇒sin^2 30∘=1/4

cos45∘=1/√2=sin45∘

cot45∘=1

⇒cot^2 45∘=1

cos60∘=1/2

⇒sec60∘=2

⇒sec^2 60∘=4

cos30∘=√3/2

⇒sec30∘=2/√3

⇒sec^2 30∘=4/3

cosec45∘=1/sin45∘=√2

⇒cosec^2 45∘=2

(sin^2 30∘+4cot45∘−sec^2 60∘)(cosec^2 45∘ sec^2 30∘)

=[(1/2)^2+4×(1)^2−(2)^2][(√2)^2×(2/√3)^2]

=1/4×8/3

=2/3.