Question

(sec2 37°- cot 2 53°) tan21° tan69°-sin51°cos39° -cos 51°sin 39°

Answer 1

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Answer 2

Answer:

Value of (sec²37°-cot²53°)tan21°tan69°-sin51°cos39°-cos51°sin39°=0

Step-by-step explanation:

Value of (sec²37°-cot²53°)tan21°tan69°-sin51°cos39°-cos51°sin39°

=[sec²(90°-53°)-cot²53°]tan21°cot(90°-21°)-sin(90°-39°)cos39°-cos(90°-39°)sin39°

=(cosec²53°-cot²53°)tan21°cot21°-cos39°cos39°-sin39°sin39°

/* we know that,

i)cosec²A-cot²A = 1,

ii)tanAcotA = 1 */

= 1×1-cos²39°-sin²39°

= 1-(cos²39°+sin²39°)

= 1-1 /*cos²A+sin²A=1*/

=0

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