Question

$sin^{2}60+cot^{2}45-2sin cos45$

Answer 1

Step-by-step explanation:

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

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Answer 2

Answer:

Step-by-step explanation:

\frac{4}{cot^{2}30\degree}+\frac{1}{sin^{2}60\degree}-cos^{2}45\degree

cot

2

30°

4

+

sin

2

60°

1

−cos

2

45°

= \frac{4}{(\sqrt{3})^{2}}+\frac{1}{\left(\frac{\sqrt{3}}{2}\right)^{2}}-\left(\frac{1}{\sqrt{2}}\right)^{2}=

(

3

)

2

4

+

(

2

3

)

2

1

−(

2

1

)

2

=\frac{4}{3}+\frac{4}{3}-\frac{1}{2}=

3

4

+

3

4

−

2

1

=\frac{8+8-3}{6}=

6

8+8−3

=\frac{13}{6}=

6

13

Therefore,

\frac{4}{cot^{2}30\degree}+\frac{1}{sin^{2}60\degree}-cos^{2}45\degree=\frac{13}{6}

cot

2

30°

4

+

sin

2

60°

1

−cos

2

45°=

6

13

•••♪