Question

sin? 45° + cosec230°-cos60° +tan? 60°
sin2 30° +cos260° + sec2 45°​

Answer 1

Answer:

-2

Explanation:

cosec2 30 sin2 45-sec2 60

\begin{lgathered}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\end{lgathered}

Cosec

2

30Sin

2

45−Sec

2

60

Cosec=

Sin

1

&Sec=

Cos

1

=

Sin

2

30

1

×Sin

2

45−

Cos

2

60

1

Cosθ=Sin(90−θ)⟹Cos60=Sin30

=

Sin

2

30

1

×Sin

2

45−

Sin

2

30

1

=

Sin

2

30

1

×(Sin

2

45−1)

Sin30=

2

1

&Sin45=

2

1

=

(

2

1

)

2

1

×((

2

1

)

2

−1)

=4×(

2

1

−1)

=4×(−

2

1

)

=−2