(1 + sec 20° + cot 70°)(1 – cosec 20° + tan70°) is

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(1 + sec 20° + cot 70°) (1 – cosec 20° + tan 70°)
= (1 + sec 20° + tan 20°) (1 – cosec 20° + cot 20°)
[∴ tan (90° – θ) = cotθ; cot (90° – θ) = tanθ]

1 +

sin20°

1 −

cos20°

sin20°

=		cos20° + 1 + sin20°			sin20° – 1 + cos20°
		cos20°			sin20°

=	(sin20° + cos20° + 1)( sin20° + cos20° + 1)
	sin20°.cos20°

=	(sin20° + cos20°)² − 1
	sin20°.cos20°

=	sin²20° + cos²20° + 2sin20°.cos20°− 1
	sin20°.cos20°

=	1 + 2sin20°.cos20°− 1	= 2
	sin20°.cos20°