Question

The value of sin64/cos26×cosec47/sec43+tan25×tan64/tan^2 30

Answer 1

we have to find the value of sin64°/cos26° × cosec47°/sec43° + tan25° × tan65°/tan²30°

solution : we know, sin(90° - x) = cosx

cosec(90° - x) = secx

tan(90° - x) = cotx

so, sin64° = sin(90° - 26°) = cos26°

cosec47° = cosec(90° - 43°) = sec43°

tan25° = tan(90° - 65°) = cot65°

now, sin64°/cos26° = cos26°/cos26° = 1

cosec47°/sec43° = sec43°/sec43° = 1

tan25° × tan65° = cot65° × tan65° = 1

so, sin64°/cos26° × cosec47°/sec43° + tan25° × tan65°/tan²30° = 1 × 1 + 1/tan²30°

= 1 + 1/(1/√3)²

= 1 + 1/(1/3)

= 1 + 3

= 4

therefore the value of sin64°/cos26° × cosec47°/sec43° + tan25° × tan65°/tan²30° is 4.

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(Sin 26 /sec 64)+(cos26/cosec64)=2

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Answer 2

Answer:

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we have to find the value of sin64°/cos26° × cosec47°/sec43° + tan25° × tan65°/tan²30°

solution : we know, sin(90° - x) = cosx

cosec(90° - x) = secx

tan(90° - x) = cotx

so, sin64° = sin(90° - 26°) = cos26°

cosec47° = cosec(90° - 43°) = sec43°

tan25° = tan(90° - 65°) = cot65°

now, sin64°/cos26° = cos26°/cos26° = 1

cosec47°/sec43° = sec43°/sec43° = 1

tan25° × tan65° = cot65° × tan65° = 1

so, sin64°/cos26° × cosec47°/sec43° + tan25° × tan65°/tan²30° = 1 × 1 + 1/tan²30°

= 1 + 1/(1/√3)²

= 1 + 1/(1/3)

= 1 + 3

= 4

therefore the value of sin64°/cos26° × cosec47°/sec43° + tan25° × tan65°/tan²30° is 4.

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