Find the value of ( sin 2 63 . + sin 2 27 . /sec 2 20 . +cot 2 70 . ) + 2 sin 36 . *sin 42 . * sec 48 . * sec 54 . .
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(sin²63°+sin²27°/sec²20°-cot²70°)+2sin36°sin42°sec48°sec54°
=[sin²63+sin²{(90°×1)-63°}/sec²20°-cot²{(90°×1)-20°}]+2sin36°sin42°
sec{(90°×1)-42°}sec{(90°×1)-36°}
=[sin²63°+cos²63°/sec²20°-tan²20°]+2sin36°sin42°cosec42°cosec36°
=1/(sec²20°-tan²20°)+2sin36°sin42°(1/sin42°)(1/sin36°)
=1+2×1×1
=1+2
=3 Ans.
[It should be sec²20°-cot²70° in the denominator]
=[sin²63+sin²{(90°×1)-63°}/sec²20°-cot²{(90°×1)-20°}]+2sin36°sin42°
sec{(90°×1)-42°}sec{(90°×1)-36°}
=[sin²63°+cos²63°/sec²20°-tan²20°]+2sin36°sin42°cosec42°cosec36°
=1/(sec²20°-tan²20°)+2sin36°sin42°(1/sin42°)(1/sin36°)
=1+2×1×1
=1+2
=3 Ans.
[It should be sec²20°-cot²70° in the denominator]
kvnmurty:
in 2nd line, it is cos²{(90°×1)-63°}.. and not sin {.. }
No. After the calculation sin will be changed to cos. If its a cos in 2 nd line then it will be sin again in the 3rd line.
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