Question

Sec70.Sin 20 + Cos 20.Cosec70 = 2
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Answer 1

★Given★

$LHS= sec70°.sin20°+cos20°.cosec70°$

and,

$RHS=2$

★Proof★

Taking LHS:

$LHS= sec70°.sin20°+cos20°.cosec70°$

$LHS= sec70°.sin(90° - 70°)+cos(90° - 70°).cosec70°$

$LHS= sec70°.cos( 70°)+sin( 70°).cosec70°$

.

[∵ sin(90°–θ)=cosθ]

[∵ cos(90°−θ)=sinθ]

.

Now, as;

[∵ secθ=1/cosθ], and

[∵ cosecθ=1/sinθ]

.

Therefore,

$LHS= \frac{1}{cos70°} .cos( 70°)+sin( 70°). \frac{1}{sin70°}$

$LHS= 1 + 1$

Since,

$LHS=2 = RHS.$

Hence, Proved