Find the value of sin²20° + cos² 20°/sec²59° - tan²59°
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Answer:
tan²x+cot²x=sec²x-1+csc²x-1=(csc²x+sec²x)-2
=>(csc²x+sec²x)-2+(csc²+sec²x)=2(csc²x+sec²x)-2=2(1/sin²x+1/cos²x)-2
=2{(sin²x+cos²x)/sin²x.cos²x}-2
=2/(sin²x.cos²x)-2
=2sec²x.csc²x-2
=>the value of expression becomes
=1+2sec²x.csc²x-2=2sec²x.csc²x-1=8/sin²2x-1
=>0<sin²2x<1=>0<8sin²2x<8=>0–1<8sin²2x-1<8–1
=>-1<the expression<7
=>It €(-1,7).Ans..
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