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.