Evaluate : sin230∘+4cot245∘−sec260∘)(cosec245∘sec230∘).

sin30∘=1/2⇒sin230∘=1/4cos45∘=1/2=sin45∘cot45∘=1⇒cot245∘=1cos60∘=1/2⇒sec60∘=2⇒sec260∘=4cos30∘=3/2⇒sec30∘=2/3⇒sec230∘=4/3cosec45∘=1/sin45∘=2⇒cosec245∘=2(sin230∘+4cot45∘−sec260∘)(cosec245∘sec230∘)=[(21)2+4×(1)2−(2)2][(2)2× (32)2]=1/4×8/3=2/3.

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Evaluate : ^{2} 30^{} + 4^{2} 45^{} - ^{2} 60^{})(cosec^{2} 45

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Evaluate : $sin^{2} 3 0^{\circ} + 4 cot^{2} 4 5^{\circ} - sec^{2} 6 0^{\circ}) (cose c^{2} 4 5^{\circ} sec^{2} 3 0^{\circ})$ .

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Evaluate :

sin^{2} 3 0^{\circ} + 4 cot^{2} 4 5^{\circ} - sec^{2} 6 0^{\circ}) (cose c^{2} 4 5^{\circ} sec^{2} 3 0^{\circ})

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Text solutionVerified

sin 3 0^{\circ} = 1/2 \Rightarrow sin^{2} 3 0^{\circ} = 1/4

cos 4 5^{\circ} = 1/ 2 = sin 4 5^{\circ}

cot 4 5^{\circ} = 1 \Rightarrow cot^{2} 4 5^{\circ} = 1

cos 6 0^{\circ} = 1/2 \Rightarrow sec 6 0^{\circ} = 2 \Rightarrow sec^{2} 6 0^{\circ} = 4

cos 3 0^{\circ} = 3 /2 \Rightarrow sec 3 0^{\circ} = 2/ 3 \Rightarrow sec^{2} 3 0^{\circ} = 4/3

cosec 4 5^{\circ} = 1/ sin 4 5^{\circ} = 2 \Rightarrow cose c^{2} 4 5^{\circ} = 2

(sin^{2} 3 0^{\circ} + 4 cot 4 5^{\circ} - sec^{2} 6 0^{\circ}) (cose c^{2} 4 5^{\circ} sec^{2} 3 0^{\circ})

= [(\frac{1}{2})^{2} + 4 \times (1)^{2} - (2)^{2}] [(2)^{2} \times (\frac{2}{3})^{2}]

= 1/4 \times 8/3

= 2/3

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Question Text	Evaluate : $sin^{2} 3 0^{\circ} + 4 cot^{2} 4 5^{\circ} - sec^{2} 6 0^{\circ}) (cose c^{2} 4 5^{\circ} sec^{2} 3 0^{\circ})$ .
Answer Type	Text solution:1
Upvotes	151

Evaluate : sin230∘+4cot245∘−sec260∘)(cosec245∘sec230∘).

Text solutionVerified

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Evaluate : $sin^{2} 3 0^{\circ} + 4 cot^{2} 4 5^{\circ} - sec^{2} 6 0^{\circ}) (cose c^{2} 4 5^{\circ} sec^{2} 3 0^{\circ})$ .